Question

The ratio of the area of two similar triangles is $9:16$, then the ratio of their corresponding sides will be ___________.

Answer 1

The ratio of areas of two similar triangles having areas $A_1$ and $A_2$ respectively is given by

$\frac{A_1}{A_2}={\left(\frac{s_1}{s_2}\right)}^2$

$\frac{9}{16}={\left(\frac{s_1}{s_2}\right)}^2$

Taking square roots on both sides, we get

$\frac{s_1}{s_2}=\frac{3}{4}$

The ratio of their corresponding sides will be $3:4$.