Question

If $∆ABC~∆QRP$, $\frac{Ar\left(ABC\right)}{Ar\left(QRP\right)}=\frac{9}{4}$, $AB=18cm$ and $BC=15cm$; then find $PR$.

Answer 1

Find the length of the side.

As we know that, the ratio of the area of two similar triangles is equal to the square of the ratio of any pair of the corresponding sides of the similar triangles.

So, the triangles $ABC$ and $PQR$ are similar are showing in the figure below.

$\frac{AreaofABC}{AreaofPQR}=\frac{9}{4}$

The length of the sides $AB$ is $18cm$ and $AB$ is $15cm$.

Find the length of $PR$ by using the following formula of area of two similar triangles,

$\Rightarrow$ $\frac{AreaofABC}{AreaofPQR}=\frac{B{C}^2}{R{P}^2}$

$\frac{9}{4}=\frac{{\left(15\right)}^2}{R{P}^2}$

$\frac{3}{2}=\frac{15}{RP}$

$3\left(RP\right)=15\left(2\right)$

$RP=\frac{30}{3}$

$RP=10cm$

Hence, the length of the side $PR$ is $10cm$.