Question

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

• A. $5\sqrt{2}cm$
• B. $2\sqrt{2}cm$
• C. $10(\sqrt{2}+1)cm$
• D. $10(\sqrt{2}-1)cm$

Answer 1

The correct option is C

$10(\sqrt{2}+1)cm$

In $\Delta$ ABC,
By Pythagoras theorem

$A{B}^2+B{C}^2=A{C}^2$
$x^2+x^2={10}^2$
$x^2=\frac{100}{2}=50$
$x=5\sqrt{2}cm$
The perimeter is $5\sqrt{2}+5\sqrt{2}+10=10(\sqrt{2}+1)$cm.