Question

If the areas of two similar triangle, $\Delta PQR$ and $\Delta XYZ$ are $162$ sq,cm and $200$ sq,cm respectively. Find the ratio of their perimeters.

Answer 1

Given that

$ar△PQR=162$

$ar△XYZ=200$

And both the triangles are similar.

$\frac{ar△PQR}{ar△XYZ}=\frac{162}{200}=\frac{81}{100}$

As we know that,

$\frac{ar△PQR}{ar△XYZ}=\frac{P{Q}^2}{X{Y}^2}$

$\frac{P{Q}^2}{X{Y}^2}=\frac{81}{100}$

$\frac{PQ}{XY}=\frac{9}{10}$

Hence, the ratio of the lengths of $△PQR$ : $△XYZ$ is $9:10$.