Question

Determine the value of x.

Answer 1

2
`√(2)`

Explanation:

A 45-90-45 triangle will have two equivalent side lengths and the hypotenuse. The hypotenuse is 4 and one of the side lengths is x. Since one of the side lengths is x, the other side length is x as well. Using the Pythagorean theorem, you can create this equation:

x^2 + x^2 = 4^2

or

2x^2 = 16

Now do the algebra:

2x^2 = 16

x^2 = 8

x = \sqrt{8\\}

which can be simplified as 2
`√(2)`