Questions: If WX=24 and WY=38, what is WZ?

Transcript text: If $W X=24$ and $W Y=38$, what is $W Z ?$

Solution

Solution Steps

Step 1: Identify the given information

We are given that WX = 24 and WY = 38. We also see that XZ is an altitude of triangle WXY, meaning it is perpendicular to WY and forms a right angle at Z.

Step 2: Recognize the relationship between the altitude and the hypotenuse

In a right triangle, the altitude to the hypotenuse is the geometric mean between the two segments it creates on the hypotenuse. In this case, XZ is the altitude, and it divides the hypotenuse WY into WZ and ZY. Therefore, the geometric mean relationship is expressed as WX² = WZ * WY.

Step 3: Solve for WZ

We are given WX = 24 and WY = 38. Substitute these values into the geometric mean formula: 24² = WZ * 38 576 = WZ * 38 WZ = 576 / 38 WZ ≈ 15.16