Question

If the areas of two similar triangles are in the ratio 9 : 64, then the ratio of their corresponding altitudes is ______.

Options

• 3 : 8

• 2 : 1

• 9 : 64

• 8 : 3

Answer 1

If the areas of two similar triangles are in the ratio 9 : 64, then the ratio of their corresponding altitudes is 3 : 8.

Explanation:

Let the areas be A₁ and A₂, and the altitudes be h₁ and h₂ respectively.

Since the triangles are similar,

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides (or altitudes).

⇒ `(A_1)/(A_2) = ((h_1)/(h_2))^2`

⇒ `(9)/(64) = ((h_1)/(h_2))^2`

⇒ `((h_1)/(h_2))^2 = (9)/(64)`

⇒ `(h_1)/(h_2) = sqrt((9)/(64))`

⇒ `(h_1)/(h_2) = 3/8`

⇒ h₁ : h₂ = 3 : 8