Question

Two similar triangles have areas $392c{m}^2$ and $200c{m}^2$ respectively. Find the ratio of any pair of corresponding sides.

Answer 1

Let $△ABC$ and $△PQR$ be two similar triangles. Let $AB$ and $PQ$ be any pair of corresponding sides.

It is given that Area $\left(△ABC\right)=392c{m}^2$ and Area $\left(△PQR\right)=200c{m}^2$

By Area theorem, the areas of two similar triangles are proportional to the squares of the corresponding sides.

$\frac{Area\left(△ABC\right)}{Area\left(△PQR\right)}=(\frac{AB}{PQ}{)}^2$

$\Rightarrow \frac{392}{200}=(\frac{AB}{PQ}{)}^2$

$\Rightarrow (\frac{AB}{PQ}{)}^2=\frac{196}{100}$

$\Rightarrow \frac{AB}{PQ}=\frac{14}{10}=\frac{7}{5}$

Hence, the ratio of the corresponding sides is $\frac{7}{5}$.