Question

In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 5 in.?

Answer 1

Hello!

since this is a 45-45-90 degree triangle the hypotenuse is a$\sqrt{2}$ where a is one of the legs

So the answer is 5$\sqrt{2}$

Hope this helps!

Answer 2

The proportions in a 45-45-90 triangle are
1 : 1 : square root 2.

Finding the length of the hypotenuse can be done with the following formula:
length of a leg × square root of 2

Therefore in a 45-45-90 triangle with legs with a length of 5 inches, the hypotenuse is
$5 \times \sqrt{2} = 5 \sqrt{2} \: in.$