# The length of a leg of an isosceles right triangle is 5sqrt2. How do you find the length of the hypotenuse?

Jan 6, 2016

The hypotenuse
$A B = 10 c m$

#### Explanation:

The above triangle is a right angled isosceles triangle , with $B C = A C$

The length of the leg given $= 5 \sqrt{2} c m$ (assuming units to be in cm)

So, $B C = A C = 5 \sqrt{2} c m$

The value of the hypotenuse $A B$ can be calculated using the Pythagoras theorem:

${\left(A B\right)}^{2} = {\left(B C\right)}^{2} + {\left(A C\right)}^{2}$

${\left(A B\right)}^{2} = {\left(5 \sqrt{2}\right)}^{2} + {\left(5 \sqrt{2}\right)}^{2}$

${\left(A B\right)}^{2} = 50 + 50$

${\left(A B\right)}^{2} = 100$

$\left(A B\right) = \sqrt{100}$

$A B = 10 c m$