Question

What is the length of x

Answer 1

Answer:

$x = 24\sqrt{3}$

y=24

z=48

Step-by-step 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 $1-1-\sqrt{2}$. Since the 45-45-90 in the picture has a side length of $24\sqrt{6}$ then its $24\sqrt{3} * \sqrt{2}$. This triangle has been multiplied by a factor of $24\sqrt{3}$.

We multiply the side length x which corresponds to 1 in the 45-45-90 triangle by $24\sqrt{3}$. This means $x=24\sqrt{3}$.

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