Question

In the diagram below, \overline{XY}

XY
is an altitude of \triangle VWX△VWX and \overline{VX}\perp\overline{WX}
VX
⊥
WX
. If VY=3VY=3, and WY=75WY=75, what is the measure of XYXY, in simplest radical form?

Answer 1

`\boxed{15}`

Explanation:

We can use the geometric mean theorem:

The altitude on the hypotenuse is the geometric mean of the two segments it creates.

In your triangle, the altitude is XY and the segments are VY and WY.

`XY = √(VY * WY) = √( 3 * 75) = √(225) = \mathbf{15}\\\text{The measure of XY is $\large \boxed{\mathbf{15}}$}`