Question

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.

Answer 1

Given: Let ΔABC = 100cm² and ΔDEF = 49cm²

Let AM = 5cm

Here, ΔABC and ΔDEF 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.

The height of the other altitude is 3.5 cm