Question

If the length of a side in a 45 ∘ − 45 ∘ − 90 ∘ triangle is x , find the length of the hypotenuse.

Answer 1

Remark

The two sides of a 45 45 90 triangle are both equal and both are x. Use the Pythagorean Theorem to find the length of the hypotenuse.

Solution

Let the hypotenuse = x

x^2 + x^2 = h^2

2x^2 = h^2 Take the square root of both sides.

sqrt(2x^2) = sqrt(h^2)

h = sqrt(2)*x or x*sqrt(2) answer