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




5√2 in.

5√5 in.

√5 in.

2√5 in.

Respuesta :

MarkV
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
[tex]5 \times \sqrt{2} = 5 \sqrt{2} \: in.[/tex]
facundo3141592

The hypotenuse of the triangle measures 5√2 in.

How to find the hypotenuse?

In a 45-45-90 triangle, both legs have the same length. So in this case we have two legs of 5 inches.

Now we can use the Pythagorean theorem to find the hypotenuse:

H^2 = (5in)^2  + (5in)^2

H = √( (5in)^2  + (5in)^2) = √(2*(5in)^2) = 5*√2 in

So the correct option is the first one, counting from the top.

If you want to learn more about right triangles, you can read:

https://brainly.com/question/2217700

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