61)

If Δ ABC∼Δ QPR,\( \rm \frac{ar(\Delta ABC)}{ar(\Delta PQR)}=\frac{4}{9}\),  AC = 12 cm, AB = 18 cm and BC = 10 cm, then PR (in cm) is equal to:

SSC CHSL 2021

A)

15

B)

8

C)

10

D)

18

62)

In a triangle ABC, the length of side AC is 4 cm less than five times the length of side AB. The length of side BC exceeds four times the length of side AB by 4 cm. If the perimeter of Δ ABC is 90 cm, then its area is:

SSC CHSL 2021

A)

180 cm²

B)

160 cm²

C)

148 cm²

D)

164 cm²

63)

The sum of three sides of an isosceles triangle is 20 cm, and the ratio of an equal side to the base is 3 ∶ 4. The altitude of the triangle is:

SSC CHSL 2021

A)

3√5 cm

B)

4√5 cm

C)

3√3 cm

D)

2√5 cm

64)

In ΔABC, P and Q are the mid-points of the sides AB and AC, respectively. R is a point on the segment PQ such that PR ∶ RQ = 1 ∶ 3. If PR = 4 cm, then BC is equal to:

SSC CHSL 2021

A)

32 cm

B)

36 cm

C)

24 cm

D)

28 cm

65)

In Δ ABC, AD is the bisector of ∠A meeting BC at D. If AB = 15 cm, BC = 10 cm and the length of BD is 2 cm less than that of DC , then the length of AC is:

SSC CHSL 2021

A)

18.5 cm

B)

18 cm

C)

22.5 cm

D)

16 cm

66)

The side QR of a triangle PQR is extended to a point S. If ∠PRS = 104° and ∠RQP =\(\frac{3}{5}\)∠QPR, then the value of ∠QPR is:

SSC CHSL 2021

A)

55°

B)

65°

C)

45°

D)

58°

67)

The area of an equilateral triangle is 10.24√3 m². Its perimeter (in m) is:

SSC CHSL 2021

A)

9.6

B)

19.2

C)

6.4

D)

3.2

68)

The sum of all the three sides of an equilateral triangle is 15√3 cm. The height of the triangle is:

SSC CHSL 2021

A)

7.5 cm

B)

7 cm

C)

9 cm

D)

8 cm

69)

In Δ ABC, AC = BC, and the length of the base AB is 10 cm. If CG = 8 cm, where G is the centroid, then what is the length of AC?

SSC CHSL 2021

A)

12 cm

B)

13 cm

C)

15 cm

D)

√91 cm

70)

In ΔABC, BD ⊥ AC at D, E is a point on BC such that ∠BEA = x°. If ∠EAC = 46° and ∠EBD = 60°, then the value of x is:

SSC CPO 2020

A)

76°

B)

72°

C)

78°

D)

68°