Question

consider triangle xyz with altitude wz. what is xz?
type the correct answer in the box. use numerals instead of words. if you need help, see this worked example
xz =

Explanation:

Step1: Apply the geometric mean theorem (altitude-on-hypotenuse theorem)

In a right - triangle, if an altitude is drawn to the hypotenuse, then the length of each leg of the right - triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.
For right - triangle \(XYZ\) with altitude \(ZW\), we have the formula \(XZ^{2}=XW\times XY\)
Given \(XW = 28 - 21=7\) and \(XY = 28\)

Step2: Substitute values into the formula

Substitute \(XW = 7\) and \(XY = 28\) into \(XZ^{2}=XW\times XY\)
We get \(XZ^{2}=7\times28\)
\(XZ^{2}=196\)

Step3: Solve for \(XZ\)

Take the square root of both sides: \(XZ=\sqrt{196}\)
\(XZ = 14\)

Answer:

14