Question

For an obtuse triangle $PQR$ as shown in the diagram above, if $PA=8$ units and area of $\Delta PQR=64$ sq. units, then $QR$ equals

• A. 16

Answer 1

The correct option is A 16
Given $\Delta PQR$ with $PA=8$ units.
And area of $\Delta PQR=64$ sq. units.
Now, we know the area of a triangle as
Area of $\Delta PQR=\frac{1}{2}\times \text{Base}\times \text{Height}$
Here, we have $PA$ as a height with $QR$ as its corresponding base.
$\Rightarrow 64=\frac{1}{2}\times QR\times PA$

$\Rightarrow 64=\frac{1}{2}\times QR\times 8$

Dividing with $8$ on both sides:

$\Rightarrow \frac{64}{8}=\frac{1}{2}\times QR$

Now, multiplying with $2$ on both sides:

$\Rightarrow 8\times 2=QR$
$\Rightarrow QR=16$ units