141)

If ΔABC ≅ ΔPQR and ∠ABC = (x + 60)°, ∠PQR = (85 - 4x)°, and ∠RPQ = (3x + 65)°, then the value of ∠ABC in degree is:

SSC CGL 2022

A)

45

B)

5

C)

15

D)

65

142)

ΔABC and ΔDEF are similar triangles and their areas are 49 cm² and 144 cm² respectively. If EF = 16.80 cm, then find BC.

SSC CGL 2022

A)

8.7 cm

B)

9.8 cm

C)

7.5 cm

D)

11.4 cm

143)

ΔABC ~ ΔDEF and the perimeters of these triangles are 32 cm and 12 cm, respectively. If DE = 6 cm, then what will be the length of AB?

SSC CGL 2022

A)

12 cm

B)

14 cm

C)

16 cm

D)

18 cm

144)

In ΔPQR, ∠Q = 90°, PQ = 8 cm and ∠PRQ = 45°. Find the length of QR.

SSC CGL 2022

A)

5 cm

B)

3 cm

C)

6 cm

D)

8 cm

145)

In ∆ ABC, D and E are points on sides AB and AC, such that DE ΙΙ BC. If AD = x + 3, DB = 2x − 3, AE = x + 1 and EC = 2x − 2, then the value of x is:

SSC CGL 2022

A)

\({{3} \over 5}\)

B)

\({{1} \over 2}\)

C)

\({{4} \over 5}\)

D)

\({{1} \over 5}\)

146)

If ∆ABC ~ ∆EDF such that AB = 6 cm, DF = 16 cm and DE = 8 cm, then the length of BC is:

SSC CGL 2022

A)

14 cm

B)

10 cm

C)

12 cm

D)

8 cm

147)

 

△ABC is a right-angle triangle at B and tan A = \(\frac{3}{4} \), then sin A + sin B + sin C will be equal to:

SSC CGL 2022

A)

\(3\frac{1}{5}\)

B)

\(2\frac{2}{5}\)

C)

\(2 \frac{4}{5}\)

D)

\(1\frac{1}{5}\)

148)

What is the ASA congruence rule of triangles, where A and S represents angle and side of triangle respectively?

SSC CGL 2022

A)

Two triangles are said to be congruent if 2 sides and the included angle of one triangle are equal to 2 sides and the included angle of the other triangle.

B)

Two triangles are said to be congruent if 2 angles and the included side of one triangle are equal to 2 angles and the included side of the other triangle.

C)

Two triangles are said to be congruent if all three sides of both the triangles are equal.

D)

Two triangles are said to be congruent if any pair of 2 angles and any 1 pair of sides of both the triangles are equal.

149)

If the areas of two isosceles triangles are in the ratio of x² ∶ y², then the ratio of their corresponding heights is:

SSC CGL 2022

A)

x³ ∶ y³

B)

\(\sqrt{x} : \sqrt{y}\)

C)

x ∶ y

D)

x² ∶ y²