Question

in this 45 45 90 triangle, given the length of a leg, how do you find the length of the hypotenuse?A) multiply the legs length by √2B) divide the legs length by √2C) multiply the legs length by 2D) hypotenuse is the same length as the given leg

Answer 1

Using Pythagorean theorem:

c² = a² + b²

where a and b are the length of the legs, and c is the length of the hypotenuse.

Given that the triangle is a 45-45-90 triangle, then both legs have the same length, that is, a = b. Then,

c² = a² + a²

c² = 2a²

√c² = √(2a²)

c = √2a

The length of the hypotenuse is found, multiplying the leg's length by √2