Question

The areas of two similar triangles are$81cm$ and $49cm$ respectively. If the altitude of the bigger triangle is$4.5cm$. Find the corresponding altitude of the smaller triangle.

Answer 1

Finding the corresponding altitude of the smaller triangle.

Given, The areas of two similar triangles are$81cm$ and $49cm$ respectively.

and, the altitude of the bigger triangle$=4.5cm$

Let $x$ be the altitude of the smaller triangle.

We know that,

The ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding altitudes.

So,$\frac{81}{49}=\frac{{4.5}^2}{x^2}$

Take square root both sides, we get

$\Rightarrow \frac{9}{7}=\frac{4.5}{x}$

$\Rightarrow x=3.5cm$

Hence, altitude of the smaller triangle is$3.5cm.$