Question

A brace for a shelf has the shape of a right triangle. Its hypotenuse is 6 inches long and the two legs are equal in length. How long are the legs of the triangle?

The legs of the triangle are both inches long.
(Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Answer 1

The legs of the triangle are
`3√(2)` inches long.

Explanation:

Pythagorean Theorem:

In a right triangle, the sum of the sides squared is equal to the hypothenuse squared, that is:

`x^2 + y^2 = h^2`

Hypotenuse is 6 inches long

This means that
`h = 6`

Two legs are equal in length.

Sides equal, so
`y = x`

How long are the legs of the triangle?

`x^2 + y^2 = h^2`

`x^2 + x^2 = 6^2`

`2x^2 = 36`

`x^2 = 18`

`x = √(18)`

`x = √(2*9)`

`x = √(2)√(9)`

`x = 3√(2)`

The legs of the triangle are
`3√(2)` inches long.