Ratio of corresponding sides of two similar triangles is 4 : 7, then find the ratio of their areas = ?

Question

Sum

Solution

Let the corresponding sides of similar triangles be s₁ and s₂.

Let A₁ and A₂ be their corresponding areas.

s₁ : s₂ = 4 : 7 ...[Given]

∴ `(s_1)/(s_2) = 4/7` ...(i)

`(A_1)/(A_2) = (s_1^2)/(s_2^2)` ...[Theorem of areas of similar triangles]

`(A_1)/(A_2) = (s_1/s_2)^2`

`(A_1)/(A_2) = (4/7)^2` ...[From (i)]

`(A_1)/(A_2) = 16/49`

∴ Ratio of areas of similar triangles = 16 : 49

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Properties of Ratios of Areas of Two Triangles

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Q 9.Q 8.Q 10.

Chapter 1: Similarity - Q.1 (B)

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SCERT Maharashtra Geometry (Mathematics 2) [English] Standard 10 Maharashtra State Board

Chapter 1 Similarity
Q.1 (B) | Q 9.

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