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Question (31)

QN0036751

A 1.5 m tall student observes that a tree casts a 6 m shadow while the student's shadow is 2 m. The height of the tree is

(A) 3 m
(B) 4 m
(C) 4.5 m
(D) 6 m

Correct Answer: C

Explanation:

Tree height/6 = 1.5/2. Therefore tree height = 4.5 m.

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Question (32)

QN0036752

If a line joining the midpoints of two sides of a triangle has length 7 cm, the third side is

(A) 3.5 cm
(B) 7 cm
(C) 14 cm
(D) 21 cm

Correct Answer: C

Explanation:

The line joining the midpoints is half the length of the third side. Hence the third side is 14 cm.

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Question (33)

QN0036753

In ΔABC, D is the midpoint of AB. A line through D parallel to BC meets AC at E. If AC = 18 cm, then AE is

(A) 6 cm
(B) 8 cm
(C) 9 cm
(D) 12 cm

Correct Answer: C

Explanation:

By the midpoint theorem, E is the midpoint of AC. Hence AE = 18/2 = 9 cm.

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Question (34)

QN0036754

In ΔABC, D and E are midpoints of AB and AC respectively. If BC = 24 cm, then DE equals

(A) 6 cm
(B) 8 cm
(C) 12 cm
(D) 16 cm

Correct Answer: C

Explanation:

The segment joining the midpoints of two sides equals half the third side. Thus DE = 12 cm.

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Question (35)

QN0036755

If ΔABC ~ ΔPQR and AD and PM are corresponding medians, then

(A) AB/AD = PQ/PM
(B) AB/PQ = AD/PM
(C) AB/PQ = PM/AD
(D) AB + AD = PQ + PM

Correct Answer: B

Explanation:

Corresponding medians of similar triangles are proportional to the corresponding sides.

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Question (36)

QN0036756

Two similar triangles have corresponding sides in the ratio 5 : 7. If a median of the smaller triangle is 10 cm, the corresponding median of the larger triangle is

(A) 12 cm
(B) 14 cm
(C) 15 cm
(D) 17.5 cm

Correct Answer: B

Explanation:

Median ratio is 5:7. Therefore 10/x = 5/7, giving x = 14 cm.

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Question (37)

QN0036757

If ΔABC ~ ΔPQR and AB = 12 cm, PQ = 18 cm, then a median AD = 8 cm corresponds to PM equal to

(A) 10 cm
(B) 12 cm
(C) 14 cm
(D) 16 cm

Correct Answer: B

Explanation:

AB/PQ = AD/PM. Hence 12/18 = 8/PM, giving PM = 12 cm.

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Question (38)

QN0036758

In two similar triangles, the ratio of corresponding sides is 3 : 4. If the perimeter of the larger triangle is 36 cm, the perimeter of the smaller triangle is

(A) 24 cm
(B) 27 cm
(C) 30 cm
(D) 32 cm

Correct Answer: B

Explanation:

Perimeters are in the ratio 3:4. Smaller perimeter = 36 × 3/4 = 27 cm.

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Question (39)

QN0036759

If ΔABC ~ ΔDEF and AB = 6 cm, BC = 8 cm, CA = 10 cm, while DE = 9 cm, then EF is

(A) 10 cm
(B) 12 cm
(C) 15 cm
(D) 18 cm

Correct Answer: B

Explanation:

Scale factor = DE/AB = 9/6 = 3/2. Therefore EF = 8 × 3/2 = 12 cm.

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Question (40)

QN0036760

In two right triangles, the hypotenuse and one corresponding side are proportional. The triangles are similar by

(A) AA
(B) SSS
(C) SAS
(D) RHS

Correct Answer: D

Explanation:

For two right triangles, proportional hypotenuse and one corresponding side give RHS similarity.

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Question (31)

A 1.5 m tall student observes that a tree casts a 6 m shadow while the student's shadow is 2 m. The height of the tree is

Explanation:

Link:

Question (32)

If a line joining the midpoints of two sides of a triangle has length 7 cm, the third side is

Explanation:

Link:

Question (33)

In ΔABC, D is the midpoint of AB. A line through D parallel to BC meets AC at E. If AC = 18 cm, then AE is

Explanation:

Link:

Question (34)

In ΔABC, D and E are midpoints of AB and AC respectively. If BC = 24 cm, then DE equals

Explanation:

Link:

Question (35)

If ΔABC ~ ΔPQR and AD and PM are corresponding medians, then

Explanation:

Link:

Question (36)

Two similar triangles have corresponding sides in the ratio 5 : 7. If a median of the smaller triangle is 10 cm, the corresponding median of the larger triangle is

Explanation:

Link:

Question (37)

If ΔABC ~ ΔPQR and AB = 12 cm, PQ = 18 cm, then a median AD = 8 cm corresponds to PM equal to

Explanation:

Link:

Question (38)

In two similar triangles, the ratio of corresponding sides is 3 : 4. If the perimeter of the larger triangle is 36 cm, the perimeter of the smaller triangle is

Explanation:

Link:

Question (39)

If ΔABC ~ ΔDEF and AB = 6 cm, BC = 8 cm, CA = 10 cm, while DE = 9 cm, then EF is

Explanation:

Link:

Question (40)

In two right triangles, the hypotenuse and one corresponding side are proportional. The triangles are similar by

Explanation:

Link:

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