Question

A parallelogram has sides $60m$ and $40m$ and one of its diagonal is $80m$ long. Then, its area is:

• A. $480m^2$
• B. $320m^2$
• C. $600\sqrt{15}{m}^2$
• D. $450\sqrt{15}{m}^2$

Answer 1

The correct option is C $600\sqrt{15}{m}^2$

We know that the diagonal of parallelogram divides into two equals parts

So, area of parallelogram $=2\left(areaoftraingleABC\right)$

Now in triangle $ABC$

$S=\frac{60+40+80}{2}=\frac{180}{2}=90$

Area of $\Delta =\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$

$=\sqrt{90\left(90-60\right)\left(90-40\right)\left(90-80\right)}$

$=\sqrt{90\times 30\times 50\times 10}$

$=300\sqrt{15}{m}^2$

Now, area of parallelogram$ABCD$$=2\times 300\sqrt{15}{m}^2$

$=600\sqrt{15}{m}^2$

Hence, $\left(C\right)$ is the required answer.