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RD Chapter 4 Triangles Ex 4.6 Solutions

Question - 1 : -
Triangles ABC and DEF are similar.
(i) If area (∆ABC) = 16 cm², area (∆DEF) = 25 cm² and BC = 2.3 cm, find EF. (C.B.S.E. 1992)
(ii) If area (∆ABC) = 9 cm², area (∆DEF) = 64 cm² and DE = 5.1 cm, find AB.
(iii) If AC = 19 cm and DF = 8 cm, find the ratio of the area of two triangles. (C.B.S.E. 1992C)
(iv) If area (∆ABC) = 36 cm², area (∆DEF) = 64 cm² and DE = 6.2 cm, find AB. (C.B.S.E. 1992)
(v) If AB = 1.2 cm and DE = 1.4 cm, find the ratio of the areas of ∆ABC and ∆DEF. (C.B.S.E. 1991C)

Answer - 1 : -


Question - 2 : - In the figure, ∆ACB ~ ∆APQ. If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area (∆ACB) : area (∆APQ).

Answer - 2 : -


Question - 3 : - The areas of two similar triangles are 81 cm² and 49 cm² respectively. Find the ratio of their corresponding heights, what is the ratio of their corresponding medians ?

Answer - 3 : -

Areas of two similar triangles are 81 cm² and 49 cm²
The ratio of the areas of two similar triangles are proportion to the square of their corresponding altitudes and also squares of their corresponding medians
Ratio in their altitudes = √81 : √49 = 9 : 7
Similarly, the ratio in their medians = √81 : √49 = 9 : 7

Question - 4 : - The areas of two similar triangles are 169 cm² and 121 cm² respectively. If the longest side of the larger triangle is 26 cm, find the longest side of the smaller triangle.

Answer - 4 : -

Triangles are similar Area of larger triangle = 169 cm²
and area of the smaller triangle =121 cm²
Length of longest sides of the larger triangles = 26 cm
Let the length of longest side of the smaller triangle = x

Question - 5 : - The areas of two similar triangles are 25 cm² and 36 cm² respectively. If the altitude of the first triangle is 2.4 cm, find the corresponding altitude of the other.

Answer - 5 : -

Area of first triangle = 25 cm²
Area of second = 36 cm²
Altitude of the first triangle = 2.4 cm
Let altitude of the second triangle = x
The triangles are similar

Question - 6 : - The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively. Find the ratio of their areas.

Answer - 6 : -

Length of the corresponding altitude of two triangles are 6 cm and 9 cm
triangles are similar

Question - 7 : - ABC is a triangle in which ∠A = 90°, AN ⊥ BC, BC = 12 cm and AC = 5 cm. Find the ratio of the areas of the ∆ANC and ∆ABC.

Answer - 7 : -

In ∆ABC, ∠A = 90°
AN ⊥ BC
BC = 12 cm, AC = 5 cm

Question - 8 : -
In the figure, DE || BC
(i) If DE = 4 cm, BC = 6 cm and area (∆ADE) = 16 cm², find the area of ∆ABC.
(ii) If DE = 4 cm, BC = 8 cm and area of (∆ADE) = 25 cm², find the area of ∆ABC. (C.B.S.E. 1991)
(iii) If DE : BC = 3 : 5, calculate the ratio of the areas of ∆ADE and the trapezium BCED

Answer - 8 : -


Question - 9 : - In ∆ABC, D and E are the mid-points of AB and AC respectively. Find the ratio of the areas of ∆ADE and ∆ABC.

Answer - 9 : - In ∆ABC, D and E are the mid points of AB and AC respectively

Question - 10 : - The areas of two similar triangles are 100 cm² and 49 cm² respectively. If the altitude of the bigger triangle is 5 cm, find the corresponding altitude of the other. (C.B.S.E. 2002)

Answer - 10 : -

∆ABC ~ ∆DEF
area ∆ABC = 100 cm²
and area ∆DEF = 49 cm²

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