Question

In an isosceles right triangle, the length of the hypotenuse is $10cm.$ Then the perimeter of the triangle is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

In $\Delta ABC,$
By Pythagoras theorem
$A{B}^2+B{C}^2=A{C}^2$
$\Rightarrow x^2+x^2={10}^2$
$\Rightarrow x^2=\frac{100}{2}=50$
$\Rightarrow x=5\sqrt{2}cm$
Hence, the perimeter is $5\sqrt{2}+5\sqrt{2}+10=10(\sqrt{2}+1)cm$