Question

Referring to the given figure, the area of $△QRS$ is

• A. $2\sqrt{5}$
• B. $10$
• C. $8\sqrt{5}$
• D. $20$

Answer 1

The correct option is D $20$

We know the formula for right angled triangle,
$Q{S}^2=Q{R}^2+S{R}^2$
$\Rightarrow {10}^2=(2x{)}^2+x^2$
$\Rightarrow 100=5x^2$
$\Rightarrow x^2=20$
Area of triangle $=$ $\frac{1}{2}\times$ base $\times$ height
$=$ $\frac{1}{2}\times 2x\times x$
$=$ $x^2$
$=20$