The length of a leg of an isosceles right triangle is $5sqrt2$ units. What is the length of the hypotenuse?

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Answer 1 · 2018-03-27T14:29:57

hypotenuse = 10

You are given the leg length of one side, so you are basically given both leg lengths because an isosceles right triangle has two equal leg lengths:

$5sqrt2$

In order to find the hypotenuse you need to do
$a^2 +b^2 =c^2$

$a$ = leg length 1
$b$ = leg length 2
$c$ = hypotenuse

$(5sqrt2)^2 + (5sqrt2)^2 = c^2$
$(25*2) +(25*2) = c^2$
$50+50 = c^2$
$100=c^2$
$sqrt100 = sqrt(c^2)$
$10 = c$
hypotenuse = 10

The length of a leg of an isosceles right triangle is 5sqrt25sqrt2 units. What is the length of the hypotenuse?