Question

Areas of two similar triangles are 225 cm² and 81 cm². If side of smaller triangle is 12 cm, find corresponding side of major triangle. 

Answer 1

Let the areas of two similar triangles be A₁ and A₂.

A₁ = 225 cm² and A₂ = 81 cm²

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

s₁ = 12 cm

`"A"_1/"A"_2 = "s"_1^2/"s"_2^2`         ...[Theorem of areas of similar triangles]

∴ `225/81 = "s"_1^2/12^2`

∴ s₁² = `(225 xx 12^2)/81`

∴ s₁ = `(15 xx 12)/9`          ...[Taking square root of both sides]

∴ s₁ = 20 cm

∴ The length of the corresponding side of the bigger triangle is 20 cm.