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

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Answer 1 · 2016-01-06T16:12:27

The hypotenuse
$AB = 10 cm$

![http://mathworld.wolfram.com/IsoscelesRightTriangle.html](useruploads.socratic.org)

The above triangle is a right angled isosceles triangle , with $BC = AC$

The length of the leg given $=5sqrt2cm$ (assuming units to be in cm)

So, $BC = AC = 5sqrt2 cm$

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

$(AB)^2 = (BC)^2 +(AC)^2$

$(AB)^2 = (5sqrt2)^2 +(5sqrt2)^2$

$(AB)^2 = 50 +50$

$(AB)^2 = 100$

$(AB) = sqrt100$

$AB = 10 cm$

The length of a leg of an isosceles right triangle is 5sqrt25sqrt2. How do you find the length of the hypotenuse?