Question 1 : The ratio of the areas of two similar triangles is $25:16$. The ratio of their perimeters is ..............

Question 2 : Triangle A has a base of x and a height of 2x. Triangle B is similar to triangle A, and has a base of 2x. What is the ratio of the area of triangle A to triangle B?

Question 3 : State true or false:<br/>The ratio of the areas of two triangles of&#160;the same height is equal to the ratio of&#160;their bases.

Question 4 : State true or false:<br/>The ratio of the areas of two triangles on&#160;the same base is equal to the ratio of&#160;their heights.

Question 6 : &#160;If the two legs of a right angled&#160;$\Delta$ are&#160;equal and the square of the hypotenuse&#160;is $100,$ then the length of each leg is:

Question 7 : In a right triangle the square of the hypotenuse is equal to twice the product of the legs. One of the acute angles of the triangle is:

Question 8 : If three sides of a right-angled triangle are integers in their lowest form, then one of its sides is always divisible by

Question 9 : Which of the following can be the sides of a right angled triangle ?

Question 10 : In $\triangle{ABC}$, $\angle{B}=90$, $AB=8\:cm$ and $BC=6\:cm$.The length of the median BM is

Question 11 : In $\Delta$ ABC, $\angle B = 90$, AB = 8 cm and BC = 6 cm. The length of the median BM is<br>

Question 12 : We use ........... formula to find the lengths of the right angled triangles.

Question 13 : In the $\triangle LMN$&#160;<b></b>$\displaystyle $, angle L is&#160;$\displaystyle { 65 }^{ o }$&#160;$\displaystyle $, angle M is a right angle, what would be angle N?

Question 14 : A............can never be made up of all odd numbers or two even numbers and one odd number.

Question 15 : Find hypotenuse of right angled triangle if the sides are $12,4\sqrt 3$

Question 16 : A right angled triangle has $24,7cm $ as its sides . What will be its hypotenuse?

Question 17 : Can we construct sets of Pythagorean Triples with all even numbers?

Question 18 : &#160;A Pythagorean Triplet always...............of all even numbers, or two odd numbers and an even number.

Question 19 : It is easy to construct sets of Pythagorean Triples, When m and n are any two ............... integers.

Question 20 : Is it true that a Pythagorean Triple can never be made up of all oddnumbers?

Question 21 : If the measures of sides of a triangle are $(x^2-1) cm, (x^2 +1) cm$, and $2x cm$, then the triangle will be:&#160;

Question 22 : In a $\Delta$ABC, if $AB^2\, =\, BC^2\, +\, AC^2$, then the right angle is at:

Question 23 : The length of the hypotenuse of a right angled $\Delta$ le whose two legs measure 12 cm and 0.35 m is:

Question 25 : Select the correct alternative and write the alphabet of that following :<br>Out of the following which is the Pythagorean triplet ?

Question 26 : If the two legs of a right angled triangle are equal and the square of the hypotenuse is $100cm^2$, then the length of each leg is _________.

Question 27 : A right-angles triangle has hypotenuse $13$ cm, one side is $12$ cm, then the third side is _________.

Question 28 : If the lengths of the sides of a triangle does not satisfy the rule of $\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$, then that triangle does not contain a

Question 29 : If the hypotenuse of a right angled triangle is 15 cm and one side of it 6cm&#160;less than the hypotenuse, the other side b is equal to.

Question 30 : Which of the following cannot be the sides a right angle triangle?<br>

Question 31 : Given the measures of the sides of the triangle , identify which measures are in the ratio 3 : 4 : 5

Question 32 : In $\Delta ABC,$ if $AB =6\sqrt{3}$ cm, $AC=12$ cm and $BC=6$ cm, then angle B is equal to:<br/>

Question 33 : <p>&#160;In a right angle triangle, the hypotenuse is the&#160;greatest side. <br/></p><b>State whether the above statement is true or false.</b><br/>

Question 34 : A man goes 40 m due north and then 50 m due west. Find his distance from the starting point.

Question 35 : A ladder $13m$ long rests against a vertical wall. If the foot of the ladder is $5m$ from the foot of the wall, find the distance of the other end of the ladder from the ground.

Question 37 : The sides of a triangle are given below.&#160;Check whether or not the sides form a right-angled triangle.$3cm, 8cm, 6cm$

Question 38 : The hypotenuse of a grassy land in the shape of a right triangle is $1$ meter more than twice the shortest side. If the third side is $7$ meters more than the shortest side, find the sides of the grassy land.

Question 39 : In $\Delta$ ABC, angle C is a right angle, then the value<br>of tan $A + tan B $is<br><br>

Question 40 : Which of the following numbers form pythagorean triplet?&#160;<br/>i) $2, 3, 4$<br/>ii) $6, 8, 10$<br/>iii) $9, 10, 11$<br/>iv) $8, 15, 17$

Question 41 : Which of the following could be the side lengths of a right triangle?

Question 42 : Triangle ABC is right -angled at C. Find&#160;BC,&#160;If AB = 9 cm and AC = 1 cm.<br/>In each case, answer correct to two place of decimal.&#160;

Question 43 : The hypotenuse 'c' and one arm 'a' of a right triangle are consecutive integers. The square of the second arm is:

Question 44 : There is a Pythagorean triplet whose one member is $6$ and other member is $10$

Question 45 : In$ \displaystyle \bigtriangleup $ ABC , angle C is a right angle, then the value of$ \displaystyle \tan A+ \tan B is $

Question 46 : The sides of a triangle are given below.&#160;Check whether or not the sides form a right-angled triangle.$13cm, 12cm, 5cm$

Question 47 : In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $b$ when $c=13 \ cm$ and $a=5 \ cm$.

Question 48 : In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find&#160;$a$ when $c=25 \ cm$ and $b=7 \ cm$.

Question 49 : The sides of a triangle are given below. Check whether or not the sides form a right angled triangle.$50cm, 80cm, 100cm$

Question 50 : $4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$<br/><b>State whether the above statement is true or false.</b><br/>

Question 51 : If $\Delta ABC \sim \Delta QRP, \displaystyle \frac{ar (ABC)}{ar (PQR)} = \frac{9}{4}, AB = 18 cm$ and $BC=15 cm$; then PR is equal to <br>

Question 52 : The sides of a triangle are in the ratio 4 : 6 : 7. Then<br>

Question 53 : If $\triangle ABC\sim \triangle QRP,\dfrac{Ar(ABC)}{Ar(QRP)}=\dfrac{9}{4}$,$AB=18\&#160;cm$&#160;and $BC=15\ cm$; then $PR$&#160;is equal to:<br/>

Question 54 : A has a pair of triangles corresponding sides proportional, and B has a pair of pentagons with corresponding sides proportional,<br>$S_1=A'$s triangles must be similar<br>$S_2=B'$s pentagons must be similar<br>Which of the following statement is correct?

Question 55 : In a right triangle, the square of the hypotenuse is $x$ times the sum of the squares of the other two sides. The value of $x$ is:<br/>

Question 56 : If corresponding sides of two similar triangles are in the ratio of $4 : 9$, then areas of these triangles are in the ratio of:

Question 57 : Aline segment DE is drawn parallel to base BC of $\Delta\,ABC$ which cuts ABat point D and AC at point E. If AB = 5 BD and EC = 3.2 cm. Find the length ofAE.

Question 58 : Through a point $P$ inside the triangle $ABC$ a line is drawn parallel to the base $AB$, dividing the triangle into two equal area. If the altitude to $AB$ has a length of $1$, then the distance from $P$ to $AB$ is

Question 59 : If $\triangle ABC\sim \triangle &#160;PQR,$ &#160;$ \cfrac{ar(ABC)}{ar(PQR)}=\cfrac{9}{4}$, &#160;$AB=18$ $cm$ and $BC=15$ $cm$, then $QR$ is equal to:

Question 60 : Instead of walking along two adjacent sides of a rectangular field,a boy book a short - cut along the diagonal of the field and saved a distance equal to 1/2 the longer side. The ratio of the shorter side of the rectangle to the longer side was:.

Question 61 : If in $\triangle $s $ABC$ and $DEF,$ $\angle A=\angle E=37^{\circ}, AB:ED=AC:EF$ and $\angle F=69^{\circ},$ then what is the value of $\angle B\: ?$<br>

Question 62 : In a $\triangle ABC$, $D$ and $E$ are the midpoints of $AB$ and $AC. DE$ is parallel to $BC$. If the area of $\Delta ABC = 60$ sq cm., then the area of the $\Delta ADE$ is equal to:<br/>

Question 63 : In $\Delta ABC$, $D$ is a point on $BC$ such that $3BD = BC$. If each side of the triangle is $12 cm$, then $AD$ equals:

Question 64 : If $A={30}^{\circ},\,a=100,\,c=100\sqrt{2}$, find the number of triangles that can be formed.

Question 65 : If $\triangle ABC$ is similar to $\triangle DEF$ such that BC=3 cm, EF=4 cm and area of $\triangle ABC=54 {cm}^{2}$. Determine the area of $\triangle DEF$.

Question 66 : State true or false:<br/>In parallelogram&#160;$&#160;ABCD&#160;$.&#160;$ E&#160;$&#160;is the mid-point of&#160;$&#160;AB&#160;$&#160;and&#160;$&#160;AP&#160;$&#160;is&#160;parallel to $&#160;EC&#160;$<b>&#160;</b>which meets&#160;$&#160;DC&#160;$&#160;at point&#160;$&#160;O&#160;$&#160;and&#160;$&#160;BC&#160;$&#160;produced at&#160;$&#160;P&#160;$. Hence$ BP= 2AD $<br/><br/><br/>

Question 67 : The hypotenuse of a right triangle is $6$ m more than twice the shortest side. If the third side is $2$ m less than the hypotenuse, find the hypotenuse of the triangle.<br>

Question 68 : Area of similar triangles are in the ratio $25:36$ then ratio of their similar sides is _________?

Question 69 : The perimeter of two similar triangles is 30 cm and 20 cm. If one altitude of the former triangle is 12 cm, then length of the corresponding altitude of the latter triangle is

Question 70 : If $\Delta ABC \sim \Delta PQR$ and $\displaystyle {{PQ} \over {AB}} = {5 \over 2}$ then area $(\Delta ABC):$ area $(\Delta PQR) = ?$

Question 71 : The altitude of an equilateral triangle of side lenght of $2\sqrt{3}$ cm is:

Question 72 : The perimeter of rectangle is $140$ cm. If the sides are in the ratio $3 : 4$, find the lengths of the four sides and the two diagonals

Question 73 : $ABCD$ is parallelogram and $P$ isthe mid point of the side $AD$. The line $BP$ meets the diagonal $AC$ in $Q$. Then the ratio $AQ:QC=$

Question 74 : Three sides of a triangle are 6 cm, 12 cm and 13 cm then<br>

Question 75 : Two triangles ABC and PQR&#160; are similar, if $BC : CA : AB = $1: 2 : 3, then $\dfrac{QR}{PR}$ is<br/>

Question 77 : Two triangles are similar and their corresponding sides are in the ratio $3 : 5$. Find the ratio of the areas of these triangles.

Question 78 : If in$\displaystyle \triangle ABC$ and$\displaystyle\triangle DEF$,$\displaystyle \frac{AB}{DE}=\frac{BC}{FD}$ then they will be similar if

Question 79 : The areas of two similar triangles are $81\ cm^{2}$ and $49\ cm^{2}$. If the altitude of the bigger triangle is $4.5\ cm$, find the corresponding altitude of the smaller triangle.

Question 80 : The sides of a triangle are $3x+4y,\,4x+3y$ and $5x+5y$ units, where $x,y&gt;0$.The triangle is ______________.

Question 81 : In quadrilateral ABCD, the diagonals AC and BD intersect each at point O. If $AO=2CO$ and $BO=2DO$; Then,$\displaystyle \Delta AOB$ is similar to $\displaystyle \Delta COD$<br/>

Question 82 : The hypotenuse of a right-angled triangle is $25 cm$. The other two sides are such that one side is $5 cm$ longer than the other side. Their lengths, in $cm$, are:

Question 83 : The areas of two similar triangles are $121$ cm$^{2}$ and $64$ cm$^{2}$, respectively. If the median of the first triangle is $12.1$ cm, then the corresponding median of the other is:<br/>

Question 84 : ABC is an isosceles triangle right angled at B. Similar triangles ACD and ABE are constructed in sides AC and AB. Find the ratio between the areas of $\triangle ABE$ and $\triangle ACD$.

Question 85 : For two triangles, if one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar. This is called ___ similarity. &#160;&#160;

Question 86 : In a triangle, sum of squares of two sides is equal to the square of the third side.

Question 87 : For $\Delta ABC$ &amp; $\Delta PQR$, if $m \angle A = m \angle R$ and $m \angle C = m \angle Q$, then $ABC \leftrightarrow$ ............. is a similarity.

Question 88 : In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point in side AC such that AP = 6 cm. Prove that $\Delta\,BPC$ is similar to $\Delta\,ABC$. Also, find the length of BP.

Question 89 : In $\triangle ABC \sim \triangle DEF$ such that $AB = 1.2\ cm$ and $DE = 1.4\ cm$. Find the ratio of areas of $\triangle ABC$ and $\triangle DEF$.

Question 90 : If all the three altitudes of a triangle are equal, the triangle is equilateral.<br/><b>State whether the above statement is true or false.</b><br/>

Question 91 : The perimeter of two similar triangle are $30\ cm$ and $20\ cm$. If one side of first triangle is $12\ cm$ determine the corresponding side of second triangle.

Question 92 : The ratio of areas of two similar triangles is $81 : 49$. If the median of the smaller triangle is $4.9\ cm$, what is the median of the other?

Question 93 : If two triangles are similar then, ratio of corresponding sides are:

Question 95 : In $\Delta ABC \sim&#160; \Delta PQR$, $M$ is the midpoint of $BC$ and $N$ is the midpoint of $QR$. If the area of $\Delta ABC =$ $100$ sq. cm and the area of $\Delta PQR =$ $144$ sq. cm. If $AM = 4$ cm, then $PN$ is:<br/>

Question 96 : $\Delta ABC$ and $\Delta DEF$ are similar and $\angle A=40^\mathring \ ,\angle E+\angle F=$

Question 97 : A right triangle has hypotenuse of length p cm and one side of length q cm. If p-q = 1, express length of the third side of the right triangle in term of p is

Question 98 : $\angle BAC$ of triangle $ABC$ is obtuse and $AB=AC$. $P$ is a point in $BC$ such that $PC= 12$ cm. $ PQ $ and $PR$ are perpendiculars to sides $AB$ and $AC$ respectively. If $PQ= 15$ cm and $=9$ cm; find the length of $PB$.<br/>

Question 99 : The lengths of the sides of a right triangle are $5x + 2$, $5x$ and $3x - 1$.&#160;If $x &gt; 0$ then the length of each side is?

Question 100 : If a triangle with side lengths as $5, 12$, and $15$ cm is similar to a triangle which has longer side length as $24$ cm, then the perimeter of the other triangle is:

Question 101 : Let&#160;$\displaystyle \Delta XYZ$ be right angle triangle with right angle at Z. Let&#160;$\displaystyle A_{X}$ denotes the area of the circle with diameter YZ. Let&#160;$\displaystyle A_{Y}$ denote the area of the circle with diameter XZ and let&#160;$\displaystyle A_{Z}$ denotes the area of the circle diameter XY. Which of the following relations is true?

Question 102 : $\frac{a}{r}$, a, ar are the sides of a triangle. If the triangle is a right angled triangle, then $r^2$ is given by

Question 103 : Match the column.<br/><table class="wysiwyg-table"><tbody><tr><td>1. In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR},\angle A=\angle P$<br/></td><td>(a) AA similarity criterion&#160;</td></tr><tr><td>2.&#160;In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \angle A=\angle P,\angle B=\angle Q$<br/><br/></td><td>(b) SAS similarity criterion&#160;</td></tr><tr><td>3.&#160;In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$<br/>$\angle A=\angle P$<br/></td><td>(c) SSS similarity criterion&#160;</td></tr><tr><td>4. In&#160;$\displaystyle \Delta ACB,DE||BC$<br/>$\displaystyle \Rightarrow \frac{AD}{BD}=\frac{AE}{CE}$<br/></td><td>(d) BPT</td></tr></tbody></table>