Question

What is the length of YA ?

Answer 1

AYZ is a right triangle (we're given that YA is perpendicular to XZ). So, we can use the pythagorean theorem to find the missing side:

`YA^2+AZ^2=YZ^2`

But we're also given
`YZ = 2AZ`, so we have

`YA^2+AZ^2=(2AZ)^2=4AZ^2`

Since AZ is half of YZ, which is 10, we deduce AZ=5.

Solving for YA, we have

`YA^2+AZ^2=4AZ^2 \iff YA^2 = 3AZ^2 \iff YA = AZ√(3) = 5√(3)`