Question

$△PQR$ is isosceles with $PQ=PR=7.5cm$ and $QR=9cm$. The height $PS$ from $P$ to $QR$, is $6cm$. Find the area of $△PQR$. What will be the height from $R$ to $PQ$ i.e. $RT$?

• A. $27c{m}^2;7.2cm$.
• B. $23c{m}^2;7.2cm$.
• C. $27c{m}^2;3.2cm$.
• D. None of these

Answer 1

The correct option is A $27c{m}^2;7.2cm$.

It is given that, $△PQR$ is isosceles triangle.

$\therefore$ $PQ=PR=7.5cm$

$PS\perp QR$ and $RT\perp PQ$ [ Given ]

$\Rightarrow$ Area of $△PQR=\frac{1}{2}\times QR\times PS$

$=\frac{1}{2}\times 9\times 6$

$=9\times 3$

$=27c{m}^2$

$\Rightarrow$ Area of $△PQR=27c{m}^2$

We can also write,

$\Rightarrow$ Area of $△PQR=\frac{1}{2}\times PQ\times RT$

$\Rightarrow$ $27=\frac{1}{2}\times 7.5\times RT$

$\Rightarrow$ $54=7.5\times RT$

$\Rightarrow$ $RT=\frac{54}{7.5}$

$\Rightarrow$ $RT=7.2cm$