The areas of two similar triangles $ABC$ and $PQR$ are in the ratio $9:16$. If $BC=4.5\ cm$, find the length of $QR$.

Given:

The areas of two similar triangles $ABC$ and $PQR$ are in the ratio $9:16$ and $BC=4.5\ cm$.

To do:

We have to find the length of $QR$.

Solution:

We know that,

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

Therefore,

$\frac{ar(\triangle ABC)}{ar(\triangle PQR)}=\frac{(BC)^2}{(QR)^2}$

$\frac{9}{16}=(\frac{4.5}{QR})^2$

$\frac{4.5}{QR}=\sqrt{\frac{9}{16}}$

$\frac{4.5}{QR}=\frac{3}{4}$

$4.5(4)=3(QR)$

$QR=\frac{18}{3}$

$QR=6\ cm$

The length of $QR$ is $6\ cm$.

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Updated on: 10-Oct-2022

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