What is the length of YA ?

Question

asked Jun 14, 2020 165k views

1 Answer

Serakfalcon · Answer 1 · 2020-06-19T20:41:18+0000

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

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