UPSC CDS 1 2022 Math Paper

Given:
The perimeter of an isosceles right triangle is 4(2+√2)cm
Formula Used:
Area of right-angled isosceles triangle =a2∕2
Where a= equal sides of the isosceles triangle
Calculation:Given, AB=BC=x (let) In △ABC,∠B=90∘
AC2=AB2+BC2
⇒AC2=x2+x2
⇒AC2=2x2
⇒AC=√2x
So, Perimeter of ABC=AB+BC+CA
⇒x+x+√2x=4(2+√‌2)
⇒2x+√‌2x=4(2+√‌2)
⇒x(2+√‌2)=4(2+√‌2)
⇒x=4
Area of triangle =x2∕2
⇒ Area of triangle =42∕2=8
∴ The area of triangle is 8 square cm .