Question

Find the perimeter of an isosceles right-angled triangle having an area of 5000 $m^2$. (use $\sqrt{2}=1.41$)

Answer 1

$\angle A=\angle C$ ( since it is a right angled isosceles triangle )

$\Rightarrow AB=BC$ ( sides opposite to equal angles are equal )

Let $AB=BC=x$

Area $=5000m^2$

$\Rightarrow \frac{1}{2}\times AB\times BC=5000m^2$

$\Rightarrow x^2=10000m^2$

$\Rightarrow x=100m$

$\Rightarrow AC=\sqrt{{100}^2+{100}^2}=100\sqrt{2}m$

$=100\times 1.41m$

$=141m$

$\Rightarrow$ Perimeter $=AB+BC+AC$

$=100+100+141$

$=341m.$

Hence, the answer is $341.$