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Question (21)

QN0036741

In ΔABC, DE || BC. If AD = 5 cm, DB = 3 cm and AC = 16 cm, then AE is

(A) 8 cm
(B) 10 cm
(C) 12 cm
(D) 13 cm

Correct Answer: B

Explanation:

AB = AD + DB = 8 cm. Hence AD/AB = AE/AC, so 5/8 = AE/16 and AE = 10 cm.

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Question (22)

QN0036742

In ΔABC, DE || BC and AD : DB = 2 : 3. If AC = 20 cm, then AE is

(A) 6 cm
(B) 8 cm
(C) 10 cm
(D) 12 cm

Correct Answer: B

Explanation:

AD/AB = 2/(2+3) = 2/5. Therefore AE/20 = 2/5, giving AE = 8 cm.

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Question (23)

QN0036743

A line parallel to one side of a triangle cuts the other two sides. If it divides one side into 6 cm and 9 cm, and the corresponding parts of the other side are x cm and 12 cm, then x is

(A) 6 cm
(B) 8 cm
(C) 9 cm
(D) 10 cm

Correct Answer: B

Explanation:

By BPT, 6/9 = x/12. Therefore x = 8 cm.

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Question (24)

QN0036744

In a trapezium ABCD, AB || DC. A line EF parallel to AB meets AD and BC at E and F. Which relation follows from the proportionality theorem?

(A) AE/ED = BF/FC
(B) AE/AD = BF/BC always equal to 1
(C) AE/ED = FC/BF
(D) AD/AE = BC/BF only

Correct Answer: A

Explanation:

Using the Basic Proportionality Theorem through the diagonal gives AE/ED = BF/FC.

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Question (25)

QN0036745

If ΔABC ~ ΔDEF and AB : DE = 2 : 3, then the ratio of their corresponding areas is

(A) 2 : 3
(B) 3 : 2
(C) 4 : 9
(D) 9 : 4

Correct Answer: C

Explanation:

The ratio of areas of similar triangles is the square of the ratio of corresponding sides. Thus 2²:3² = 4:9.

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Question (26)

QN0036746

Two similar triangles have areas 64 cm² and 100 cm². The ratio of their corresponding sides is

(A) 8 : 10
(B) 16 : 25
(C) 4 : 5
(D) 3 : 5

Correct Answer: C

Explanation:

Side ratio = √(64/100) = 8/10 = 4/5.

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Question (27)

QN0036747

Two similar triangles have corresponding sides in the ratio 2 : 5. If the smaller triangle has area 24 cm², the area of the larger triangle is

(A) 60 cm²
(B) 120 cm²
(C) 150 cm²
(D) 180 cm²

Correct Answer: C

Explanation:

Area ratio = 2²:5² = 4:25. Larger area = 24 × 25/4 = 150 cm².

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Question (28)

QN0036748

A 6 m pole casts a 4 m shadow. At the same time, a tower casts a 28 m shadow. Assuming the same conditions, the tower's height is

(A) 36 m
(B) 40 m
(C) 42 m
(D) 48 m

Correct Answer: C

Explanation:

Height/shadow is constant. Tower height/28 = 6/4, so tower height = 42 m.

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Question (29)

QN0036749

A vertical object 2 m high casts a shadow 1.5 m long. At the same time, a building casts a shadow 12 m long. The building height is

(A) 12 m
(B) 14 m
(C) 16 m
(D) 18 m

Correct Answer: C

Explanation:

Building height/12 = 2/1.5. Therefore building height = 16 m.

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Question (30)

QN0036750

A girl 0.9 m tall walks 4.8 m away from a lamp post of height 3.6 m. If her shadow is x metres long, then x is

(A) 1.2 m
(B) 1.6 m
(C) 2.4 m
(D) 3.2 m

Correct Answer: B

Explanation:

By similar triangles, (4.8 + x)/x = 3.6/0.9 = 4. Hence 3x = 4.8 and x = 1.6 m.

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Question (21)

In ΔABC, DE || BC. If AD = 5 cm, DB = 3 cm and AC = 16 cm, then AE is

Explanation:

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Question (22)

In ΔABC, DE || BC and AD : DB = 2 : 3. If AC = 20 cm, then AE is

Explanation:

Link:

Question (23)

A line parallel to one side of a triangle cuts the other two sides. If it divides one side into 6 cm and 9 cm, and the corresponding parts of the other side are x cm and 12 cm, then x is

Explanation:

Link:

Question (24)

In a trapezium ABCD, AB || DC. A line EF parallel to AB meets AD and BC at E and F. Which relation follows from the proportionality theorem?

Explanation:

Link:

Question (25)

If ΔABC ~ ΔDEF and AB : DE = 2 : 3, then the ratio of their corresponding areas is

Explanation:

Link:

Question (26)

Two similar triangles have areas 64 cm² and 100 cm². The ratio of their corresponding sides is

Explanation:

Link:

Question (27)

Two similar triangles have corresponding sides in the ratio 2 : 5. If the smaller triangle has area 24 cm², the area of the larger triangle is

Explanation:

Link:

Question (28)

A 6 m pole casts a 4 m shadow. At the same time, a tower casts a 28 m shadow. Assuming the same conditions, the tower's height is

Explanation:

Link:

Question (29)

A vertical object 2 m high casts a shadow 1.5 m long. At the same time, a building casts a shadow 12 m long. The building height is

Explanation:

Link:

Question (30)

A girl 0.9 m tall walks 4.8 m away from a lamp post of height 3.6 m. If her shadow is x metres long, then x is

Explanation:

Link:

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