Question

I really need help please!!

Answer 1

Using similar triangles, we see that 12/x = x/16.  Multiplying by 16x, we see that x^2=12*16=192.

By the Pythagorean Theorem, $12^2+y^2=x^2$.  Since x^2=192, we know that $144+y^2=192$.  Subtracting 144 from both sides, we see that $y^2=48$, so y=$4 \sqrt{3}$.