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

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