ML Aggarwal Similarity MCQs Class 10 ICSE Maths Solutions Ch-13. We Provide Step by Step Answer of MCQs Questions for Ch-13 Similarity as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-10.

## ML Aggarwal Similarity MCQs Class 10 ICSE Maths Solutions Ch-13

Board | ICSE |

Subject | Maths |

Class | 10th |

Chapter-13 | Similarity |

Writer / Book | Understanding |

Topics | Solutions of MCQs |

Academic Session | 2024-2025 |

### Similarity MCQs

ML Aggarwal Class 10 ICSE Maths Solutions Ch-13

**Question 1 ****In the adjoining figure, ∆ABC ~ ∆QPR. Then ∠R is **

**(a) 60° **

**(b) 50°**

**(c) 70°**

**(d) 80°**

**Answer 1**

In the given figure,

∆ABC ~ ∆QPR

∴ ∠A = ∠Q, ∠B = ∠P and ∠C = ∠R

But ∠A = 70°, ∠B = 50°

∴ ∠C = 180° – (70° + 500) = 180° – 120° = 60°

∠C = ∠R

∴ ∠R = ∠C = 60°

Page 291

**Question 2 ****In the adjoining figure, ∆ABC ~ ∆QPR. The value of x is **

**(a) 2.25 cm**

**(b) 4 cm**

**(c) 4.5 cm**

**(d) 5.2 cm**

**Answer 2**

In the given figure

∆ABC ~ ∆QPR

AC/QR = BC?PR

6/3 = 4.5/x

x= (3 x 4.5)/6

= 2.25

x = 2.25 cm

**Question 3 ****In the adjoining figure, two line segments AC and BD intersect each other at the point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠APB = 50° and ∠CDP = 30°. Then, ∠PBA is equal to**

**(a) 50°**

**(b) 30°**

**(c) 60°**

**(d) 100°**

**Answer 3**

In the given figure two line segments AC and BD intersect each other at P

and PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠APB = 50° and ∠CDP = 30°

In ∆APB and ∆CPD

**Question 4 ****In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE, then the two triangles are**

**(a) congruent but not similar**

**(b) similar but not congruent**

**(c) neither congruent nor similar**

**(d) congruent as well as similar**

**Answer 4**

In ∆ABC and ∆DEF

∠B = ∠E, ∠F = ∠C

AB = 3DE

∵ Two angles of the one triangles are equal

to corresponding two angles of the other

But sides are not equal

∵ Triangles are similar but not congruent, (b)

**Question 5 ****The adjoining figure, AB || DE. The length of CD is**

**(a) 2.5 cm**

**(b) 2.7 cm**

**(c) 10/ 3 cm**

**(d) 3.5 cm**

**Answer 5**

In the given figure, AB || DE

∆ABC ~ ∆DCE

AB/DE = BC/CD

5/3 = 4.5/CD

CD = (3 x 4.5)/5

2.7 cm

**Question 6 ****If ∆PQR ~ ∆ABC, PQ = 6 cm, AB = 8 cm and perimeter of ∆ABC is 36 cm, then perimeter of ∆PQR is**

**(a) 20.25 cm**

**(b) 27 cm**

**(c) 48 cm**

**(d) 64 cm**

**Answer 6**

∆PQR ~ ∆ABC

PQ = 6 cm, AB = 8 cm

Perimeter of ∆ABC = 36 cm

Let perimeter of ∆PQR be x cm

= 27 cm

**Question 7 ****In the adjoining figure, DE || BC and all measurements are in centimeters. The length of AE is**

**(a) 2 cm**

**(b) 2.25 cm**

**(c) 3.5 cm**

**(d) 4 cm**

**Answer 7 **

In the given figure,

DE || BC

**Question 8 ****In the given figure, PQ || CA and all lengths are given in centimeters. The length of BC is**

**(a) 6.4 cm**

**(b) 7.5 cm**

**(c) 8 cm**

**(d) 9 cm**

**Answer 8**

In the given figure,

PQ || CA

Let BC = x

Page 292

**Question 9**

**In the given figure, MN || QR. If PN = 3.6 cm, NR = 2.4 cm and PQ = 5 cm, then PM is**

**(a) 4 cm**

**(b) 3.6 cm**

**(c) 2 cm**

**(d) 3 cm**

**Answer 9**

In the given figure, MN || QR

PN = 3.6 cm, NR = 2.4 cm and PQ = 5 cm

Let PM = x cm

#### Question 10 **It is given that ∆ABC ~ ∆PQR with BC/QR=1/3 area of ΔPQR/area of ΔABC then equal to**

**(a) 9**

**(b) 3**

**(c) 1/3**

**(d) 1/9**

**Answer 10**

∆ABC ~ ∆PQR

BC/QR=1/3

**Question 11 ****If the areas of two similar triangles are in the ratio 4 : 9, then their corresponding sides are in the ratio**

**(a) 9 : 4**

**(b) 3 : 2**

**(c) 2 : 3**

**(d) 16 : 81**

**Answer 11**

Ratio in the areas of two similar triangles = 4 : 9

Ratio in their corresponding sides

= √4 : √9

= 2 : 3 (c)

**Question 12 ****If ∆ABC ~ ∆PQR, BC = 8 cm and QR = 6 cm, then the ratio of the areas of ∆ABC and ∆PQR is**

**(a) 8 : 6**

**(b) 3 : 4**

**(c) 9 : 16**

**(d) 16 : 9**

**Answer 12**

#### ∆ABC ~ ∆PQR, BC = 8 cm, QR = 6 cm

area of ΔABC/area of ΔPQR=BC²/QR²

8²/6² = 64/36 = 16/9 (d)

**Question 13 ** **If ∆ABC ~ ∆QRP area of ΔABC/area of ΔPQR= 9/4 AB = 18 cm and BC = 15 cm, then the length of PR is equal to**

(a) 10 cm

(b) 12 cm

(c) 20/3

(d) 8 cm

(a) 10 cm

(b) 12 cm

(c) 20/3

(d) 8 cm

**Answer 13**

∆ABC ~ ∆QRP

area of ΔABC/area of ΔPQR

**Question 14 ****If ∆ABC ~ ∆PQR, area of ∆ABC = 81 cm², area of ∆PQR = 144 cm² and QR = 6 cm, then length of BC is**

**(a) 4 cm**

**(b) 4.5 cm**

**(c) 9 cm**

**(d) 12 cm**

**Answer 14**

∆ABC ~ ∆PQR,

area of ∆ABC = 81 cm² and area of ∆PQR = 144 cm²,

QR = 6 cm, BC = ?

**Question 15 ****In the given figure, DE || CA and D is a point on BD such that BD : DC = 2 : 1. The ratio of area of ∆ABC to area of ∆BDE is**

**(a) 4 : 1**

**(b) 9 : 1**

**(c) 9 : 4**

**(d) 3 : 2**

**Answer 15**

In the given figure, DE || CA ,

D is a point on BC and BD : DC = 2 : 1

BD : BC = 2 : (2 + 1) = 2 : 3

In ∆ABC, DE || CA

∆ABC ~ ∆BDE

**Question 16 ****If ABC and BDE are two equilateral triangles such that D is mid-point of BC, then the ratio of the areas of triangles ABC and BDE is**

**(a) 2 : 1**

**(b) 1 : 2**

**(c) 1 : 4**

**(d) 4 : 1**

**Answer 16**

∆ABC and ∆BDE are an equilateral triangles

**Question 17 ****The areas of two similar triangles are 81 cm² and 49 cm² respectively. If an altitude of the smaller triangle is 3.5 cm, then the corresponding altitude of the bigger triangle is**

**(a) 9 cm**

**(b) 7 cm**

**(c) 6 cm**

**(d) 4.5 cm**

**Answer 17**

Areas of two similar triangles are 81 cm² and 49 cm²

The altitude of the smaller triangle is 3.5 cm

Let the altitude of the bigger triangle is x, then

**Question 18 ****Given ∆ABC ~ ∆PQR, area of ∆ABC = 54 cm² and area of ∆PQR = 24 cm². If AD and PM are medians of ∆’s ABC and PQR respectively, and length of PM is 10 cm, then length of AD is**

**(a) 49/3 cm**

**(b) 20/3 cm**

**(c) 15 cm**

**(d) 22.5 cm**

**Answer 18**

∆ABC ~ ∆PQR

area of ∆ABC = 54 cm²

and of ∆PQR = 24 cm²

AD and PM are their median respectively

PM = 10 cm

Let AD = x cm, then

— : End of ML Aggarwal Similarity MCQs Class 10 ICSE Maths Solutions Ch-13 :–

Return to: ML Aggarwal Solutions for ICSE Class-10

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