Question

P (2, 1), Q (2, 5) and R (k, 5) are the three vertices of $\Delta PQR$ in which $\angle Q={90}^{\circ }$. If the area of $\Delta PQR$ is $10$ unit square , the value of "k" is:

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

The correct option is C 7

$QR=k-2$
$PQ=4$
$Area=\frac{1}{2}\times QR\times PQ$
$10=\frac{1}{2}\times (k-2)\left(4\right)$
$5=k-2$
$k=7$