Question

What is the length of x

Answer 1

`x = 24√(3)`

y=24

z=48

Explanation:

To find x, y, and z, use special triangles 45-45-90 and 30-60-90. A 45-45-90 triangle has standard side lengths
`1-1-√(2)`. Since the 45-45-90 in the picture has a side length of
`24√(6)` then its
`24√(3) * √(2)`. This triangle has been multiplied by a factor of
`24√(3)`.

We multiply the side length x which corresponds to 1 in the 45-45-90 triangle by
`24√(3)`. This means
`x=24√(3)`.

The other triangle is a 30-60-90 special triangle which has side lengths
`1-√(3) -2`. x corresponds to the
`√(3)` side length. This means y corresponds to the side length 1. This means y is 24 from
`24√(3)`. And z is the final side length which corresponds to side length 2. So it is 48 or 2*24=48.