Question

The areas of two similar triangles are 81 cm² and 49 cm² respectively. If the altitude of the first triangle is 6.3 cm, find the corresponding altitude of the other.

Answer 1

Given: Let △ABC = 81cm² and △DEF = 49cm²

Let AM = 6.3cm

Here, △ABC and △DEF are similar triangles

We know that, in similar triangles, corresponding angles are in the same ratio.

⇒∠B = ∠E and ∠C = ∠F …(i)

In △ABM and △DEN

∠B = ∠E [from (i)]

and ∠M = ∠N [each 90°]

∴ △ABC ~ △DEF [by AA similarity]

So, AM/DN = AB/DE = BM/EN …(ii)

We know that, the ratio of two similar triangles is equal to the square of the ratio of their corresponding sides.

Height of the other altitude is 4.9 cm