Question

In a right- angled triangle, the two sides that form the right angle are both 5 inches. How do you find the length of the other side (the hypotenuse)?

Answer 1

`5 sqrt(2)` inches

Explanation:

Given: A right triangle with two sides `5` inches.

To find the hypotenuse you can use the Pythagorean Theorem:

`5^2 + 5^2 = h^2`, where `h` is the hypotenuse

`h = sqrt(25 + 25) = sqrt(50) = sqrt(25 * 2) = sqrt(25)sqrt(2) = 5 sqrt(2)`

The other way to solve is to realize that a `45^@-45^@-90^@` triangle has the side proportions: `1:1:sqrt(2)`

This means if the sides are `5` inches, the sides would be: `5:5:5sqrt(2)`