Question

In the diagram $\Delta ABC$ is right angled at $C$. Also, $M,NandP$ are the mid points of sides $BC,ACandAB$ respectively. If the area of $\Delta APN$ is $2sq.cm$, then the area of $\Delta ABC$ in $sq.cm$ is

• A. $8$
• B. $12$
• C. $16$
• D. $4$

Answer 1

The correct option is A $8$

Let $AN=NC=x$

and $MC=MB=y$
Area of $\Delta APN=2$
$\frac{1}{2}\times PN\times AN=2$
$PN\times AN=4$
$PN=\frac{4}{x}$
$y=\frac{4}{x}$ [$\because MC=yandPN=y$]
$xy=4$
Area of $\Delta ABC=\frac{1}{2}\times BC\times AC$ [$\because BC=2MC=2yandAC=2x$]
$=\frac{1}{2}\times 2y\times 2x$
$=2xy=2\left(4\right)=8c{m}^2$.