Question

Question 87

In the given figure, area of $\Delta PQR$ is $20c{m}^2$ and area of $\Delta PQS$ is $44c{m}^2$. Find the length RS, if PQ is perpendicular to QS and QR is 5 cm.

Answer 1

Given, area of $\Delta PQR=20c{m}^2$ and area of $\Delta PQS=44c{m}^2$
We know that,
Area of triangle $=\frac{1}{2}\times Base\times Height.$

$\therefore$ Area of $\Delta PQR=\frac{1}{2}\times PQ\times QR$
$\Rightarrow 20=\frac{1}{2}\times PQ\times 5\Rightarrow \frac{20\times 2}{5}=PQ[\because$ QR = 5 cm, given]
$\Rightarrow PQ=8cm$
$\therefore$ Area of $\Delta PQS=\frac{1}{2}\times PQ\times QS$
$\Rightarrow 44=\frac{1}{2}\times 8\times QS\Rightarrow QS=\frac{44\times 2}{8}[\because PQ=8cm]$
$\Rightarrow QS=11cm$
Now, RS = QS - QR = 11 - 5 = 6 cm