Question

In 45-45-90 right triangle, where the length of the hypotenuse is `15sqrt2`,What is the length on one of the legs?

Answer 1

`a = b = 15`

Explanation:

That right triangle is also isosceles - both sides are the same length. So, using the Pythagorean Theorem:
`h^2 = a^2 + b^2`
`(15sqrt(2))^2 = a^2 + b^2 = 2a^2 = 2b^2`
`450 = 2a^2` ; `a = b = 15`