{"id":37265,"date":"2019-11-08T17:53:18","date_gmt":"2019-11-08T12:23:18","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=37265"},"modified":"2019-11-08T17:53:18","modified_gmt":"2019-11-08T12:23:18","slug":"cat-questions-on-similarity-of-triangles","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/cat-questions-on-similarity-of-triangles\/","title":{"rendered":"CAT Questions on Similarity of Triangles"},"content":{"rendered":"

CAT Questions on Similarity of Triangles<\/strong><\/span><\/h2>\n

Download important Similarity of triangle Questions for CAT PDF based on previously asked questions in CAT exam. Practice Similarity of triangle Questions PDF for CAT exam.<\/p>\n

Download CAT Questions on Similarity of Triangles<\/a><\/p>\n

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Question 1:\u00a0<\/b>In two similar triangles ABC and MNP, if AB = 2.25 cm, MP = 4.5 cm and PN = 7.5 cm and m \u2220ACB = m \u2220MNP and m \u2220ABC = m \u2220MPN, then the length of side BC , in cm, is<\/p>\n

a)\u00a04.5<\/p>\n

b)\u00a03.75<\/p>\n

c)\u00a04.75<\/p>\n

d)\u00a03.5<\/p>\n

Question 2:\u00a0<\/b>The perimeters of two similar triangles \u0394ABC andCare 36cm and 24 cm respectively. If PQ = 10 cm, then AB is:<\/p>\n

a)\u00a025 cm<\/p>\n

b)\u00a010 cm<\/p>\n

c)\u00a015 cm<\/p>\n

d)\u00a020 cm<\/p>\n

Question 3:\u00a0<\/b>\u0394 ABC and \u0394 DEF are similar triangles. Length of AB is 10 cm and length of the corresponding side DE is 6 cm. What is the ratio of Perimeter of \u0394ABC to \u0394DEF?<\/p>\n

a)\u00a05:3<\/p>\n

b)\u00a03:5<\/p>\n

c)\u00a025:9<\/p>\n

d)\u00a09:25<\/p>\n

Question 4:\u00a0<\/b>Triangle \u0394XYZ is similar to \u0394PQR. If XY:PQ=5:1. If Area of \u0394PQR is 5 sq cm, what is the area (in sq cm) of \u0394XYZ?<\/p>\n

a)\u00a0125<\/p>\n

b)\u00a0120<\/p>\n

c)\u00a0100<\/p>\n

d)\u00a064<\/p>\n

Question 5:\u00a0<\/b>The perimeter of two similar triangles ABC and PQR are 36 cms and 24 cms respectively. If PQ = 10 cm then the length of AB is<\/p>\n

a)\u00a018 cm<\/p>\n

b)\u00a012 cm<\/p>\n

c)\u00a015 cm<\/p>\n

d)\u00a030 cm<\/p>\n

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Question 6:\u00a0<\/b>\u2206ABC and \u2206DEF are two similar triangles and the perimeter of \u2206ABC and \u2206DEF are 30 cm and 18 cm respectively. If length of DE = 36 cm, then length of AB is<\/p>\n

a)\u00a060 cm<\/p>\n

b)\u00a040 cm<\/p>\n

c)\u00a045 cm<\/p>\n

d)\u00a050 cm<\/p>\n

Question 7:\u00a0<\/b>Consider the following figure shown below and choose which of the following equation is correct about the similarity of both triangles?<\/p>\n

<\/figure>\n

a)\u00a0\u25b3PQR-\u25b3EFD<\/p>\n

b)\u00a0\u25b3PQR-\u25b3DEF<\/p>\n

c)\u00a0\u25b3PQR-\u25b3FDE<\/p>\n

d)\u00a0\u25b3RQP-\u25b3DFE<\/p>\n

Question 8:\u00a0<\/b>Which of the following condition is TRUE about the similarity of triangle ABC and DEF given below?<\/p>\n

<\/figure>\n

a)\u00a0$\\angle A=\\angle D, \\angle B=\\angle E, \\angle C=\\angle F$<\/p>\n

b)\u00a0$\\angle A=\\angle E, \\angle B=\\angle D, \\angle C=\\angle F$<\/p>\n

c)\u00a0$\\angle A=\\angle F, \\angle B=\\angle D, \\angle C=\\angle E$<\/p>\n

d)\u00a0None of these<\/p>\n

Question 9:\u00a0<\/b>Which of the following options is\/are CORRECT about the similarity of the two triangles?<\/p>\n

a)\u00a0The corresponding sides are proportional to each other.<\/p>\n

b)\u00a0The corresponding angles are equal.<\/p>\n

c)\u00a0The corresponding sides may or may not be equal to each other.<\/p>\n

d)\u00a0All option are correct.<\/p>\n

Question 10:\u00a0<\/b>If area of similar triangles \u0394 ABC and \u0394 DEF be 64 sq cm and 121 sq cm and EF = 15.4 cm then BC equals:<\/p>\n

a)\u00a08 cm<\/p>\n

b)\u00a018 cm<\/p>\n

c)\u00a011.2 cm<\/p>\n

d)\u00a08.2 cm<\/p>\n

Question 11:\u00a0<\/b>Triangle $ABC$ is similar to triangle $PQR$ and $AB : PQ = 2 : 3. AD$ is the median to the side $BC$ in triangle $ABC$ and $PS$ is the median to the side $QR$ in triangle $PQR.$ What is the value of $(\\frac{BD}{QS})^2$?<\/p>\n

a)\u00a0$\\frac{3}{5}$<\/p>\n

b)\u00a0$\\frac{4}{9}$<\/p>\n

c)\u00a0$\\frac{2}{3}$<\/p>\n

d)\u00a0$\\frac{4}{7}$<\/p>\n

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Answers & Solutions:<\/strong><\/span><\/p>\n

1)\u00a0Answer\u00a0(B)<\/strong><\/p>\n

As we can see, the 2 triangles are similar. Their sides are in the ratio 2:1 (MPN: ABC). Hence, BC will be 7.5\/2 = 3.75 cm. Option B is the right answer.<\/p>\n

2)\u00a0Answer\u00a0(C)<\/strong><\/p>\n

In Similar triangles , corresponding sides are of same proportion.
\n$\\frac{ Perimeter \u0394ABC }{ Perimeter \u0394PQR }=\\frac{AB}{PR}$
\n$\\frac{ 36 }{ 24 }=\\frac{AB}{10}$
\nAb = 15
\n<\/span><\/p>\n

3)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

It is given that \u0394AB $\\sim$ \u0394DEF<\/p>\n

Also, length of AB = 10 cm and length of the corresponding side DE = 6 cm<\/p>\n

=> Ratio of Perimeter of \u0394ABC : Perimeter of \u0394DEF = Ratio of corresponding sides = AB : DE<\/p>\n

=\u00a0$\\frac{10}{6} = \\frac{5}{3}$<\/p>\n

$\\therefore$ The required ratio is 5 : 3<\/p>\n

=> Ans – (A)<\/p>\n

4)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

Given\u00a0: $\\triangle XYZ \\sim \\triangle PQR$ and\u00a0XY:PQ=5:1<\/p>\n

To find\u00a0: ar($\\triangle$ XYZ) =\u00a0$x$ = ?<\/p>\n

Solution : Ratio of areas of two similar triangles is equal to the ratio of square of the corresponding sides.<\/p>\n

=> $\\frac{ar(\\triangle XYZ)}{ar(\\triangle PQR)}=(\\frac{XY}{PQ})^2$<\/p>\n

=> $\\frac{x}{5}=(\\frac{5}{1})^2$<\/p>\n

=> $\\frac{x}{5}=\\frac{25}{1}$<\/p>\n

=> $x=25\\times5=125$ $cm^2$<\/p>\n

=> Ans – (A)<\/p>\n

5)\u00a0Answer\u00a0(C)<\/strong><\/p>\n

It is given that \u0394ABC $\\sim$ \u0394PQR<\/p>\n

Also, perimeter of \u2206ABC and \u2206PQR are 36 cm and 24 cm<\/p>\n

=> Ratio of Perimeter of \u0394ABC : Perimeter of \u0394PQR = Ratio of corresponding sides = AB : PQ<\/p>\n

=\u00a0$\\frac{36}{24} = \\frac{AB}{10}$<\/p>\n

=> AB = $\\frac{3}{2} \\times 10=15$ cm<\/p>\n

=> Ans – (C)<\/p>\n

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6)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

It is given that \u0394ABC $\\sim$ \u0394DEF<\/p>\n

Also, perimeter of \u2206ABC and \u2206DEF are 30 cm and 18 cm<\/p>\n

=> Ratio of Perimeter of \u0394ABC : Perimeter of \u0394DEF = Ratio of corresponding sides = AB : DE<\/p>\n

=\u00a0$\\frac{30}{18} = \\frac{AB}{36}$<\/p>\n

=> AB = $\\frac{5}{3} \\times 36=60$ cm<\/p>\n

=> Ans – (A)<\/p>\n

7)\u00a0Answer\u00a0(B)<\/strong><\/p>\n

If we compare the corresponding sides of two triangles,=> $\\frac{PQ}{DE}=\\frac{2.5}{5}=\\frac{1}{2}$<\/p>\n

Similarly, $\\frac{QR}{EF}=\\frac{PR}{DF}=\\frac{1}{2}$<\/p>\n

Since, ratio of all corresponding sides is equal, then $\\triangle PQR \\sim \\triangle DEF$<\/p>\n

=> Ans – (B)<\/p>\n

8)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

The ratio of sides in $\\triangle$ ABC and\u00a0$\\triangle$\u00a0DEF<\/p>\n

= $\\frac{AB}{DE}=\\frac{BC}{EF}=\\frac{AC}{DF}$<\/p>\n

= $\\frac{14}{7}=\\frac{8}{4}=\\frac{10}{5}=\\frac{2}{1}$<\/p>\n

Since, the ratio of corresponding sides are equal, =>\u00a0$\\triangle$\u00a0ABC $\\sim$\u00a0$\\triangle$\u00a0DEF<\/p>\n

$\\therefore$\u00a0$\\angle A=\\angle D, \\angle B=\\angle E, \\angle C=\\angle F$<\/p>\n

=> Ans – (A)<\/p>\n

9)\u00a0Answer\u00a0(D)<\/strong><\/p>\n

If two triangles are similar, then the corresponding sides are proportional to each other. Also, the corresponding angles are equal, but the corresponding sides may or may not be equal to each other. Thus, all are correct.<\/p>\n

=> Ans – (D)<\/p>\n

10)\u00a0Answer\u00a0(C)<\/strong><\/p>\n

Area of\u00a0\u0394 ABC = 64 sq.cm
\nArea of\u00a0\u0394 DEF = 121 sq.cm
\nGiven that\u00a0\u0394 ABC and\u00a0\u0394 DEF are similar triangles.
\nThen, $\\dfrac{\\text{Area of\u00a0 } \\triangle ABC}{\\text{Area of\u00a0 } \\triangle DEF} = (\\dfrac{BC}{EF})^2$<\/p>\n

=> $\\dfrac{64}{121} = (\\dfrac{BC}{15.4})^2$<\/p>\n

=> $\\dfrac{BC}{15.4} = \\dfrac{8}{11}$<\/p>\n

=> $BC = \\dfrac{8}{11}\\times15.4 = 11.2 cm$<\/p>\n

11)\u00a0Answer\u00a0(B)<\/strong><\/p>\n

In the case of similar triangles AB\/PQ =AC\/PR =BC\/QR
\nAB\/PQ=2\/3
\nAB\/PQ=BC\/QR
\nAB\/PQ=2BD\/2QS
\nAB\/PQ=BD\/QS
\nBD\/QS=2\/3
\n$(\\frac{BD}{QS})^2$=4\/9<\/p>\n

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We hope this Similarity of triangles Questions PDF for CAT with Solutions will be helpful to you.<\/p>\n","protected":false},"excerpt":{"rendered":"

CAT Questions on Similarity of Triangles Download important Similarity of triangle Questions for CAT PDF based on previously asked questions in CAT exam. Practice Similarity of triangle Questions PDF for CAT exam. Download CAT Quant Questions PDF Take 3 Free Mock Tests for CAT Question 1:\u00a0In two similar triangles ABC and MNP, if AB = […]<\/p>\n","protected":false},"author":42,"featured_media":37270,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[3,169,125,350,362,366],"tags":[1713,2967],"class_list":{"0":"post-37265","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-cat","8":"category-downloads","9":"category-featured","10":"category-iift","11":"category-snap","12":"category-xat","13":"tag-cat-2019","14":"tag-similarity-of-triangles-questions-for-cat"},"better_featured_image":{"id":37270,"alt_text":"CAT Questions on Similarity of Triangles","caption":"CAT Questions on Similarity of Triangles\n","description":"CAT Questions on Similarity of 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