Question

A 45-45-90 triangle has a hypotenuse of length 14 units. What is the length of one of the legs?

Answer 1

`7sqrt(2)` units

Explanation:

A 45-45-90 triangle is a right triangle whose legs are the same length. Let `l` be that length. The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of its legs. Applying this, we have:

`l^2 + l^2 = 14^2`

`=> 2l^2 = 14^2`

`=> l^2 = 14^2/2`

`=> l = 14/sqrt(2) = 7sqrt(2)`