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:

Identify given values

We have right triangle \(XYZ\) with \(\angle XZY = 90^\circ\).
The altitude to the hypotenuse is \(WZ\).
The hypotenuse length is \(XY = 28\).
The segment length is \(WY = 21\).

Calculate remaining segment

Find the length of segment \(XW\).

$$ XW = XY - WY = 28 - 21 = 7 $$

Apply geometric mean theorem

Use the leg rule for right triangles.
The leg \(XZ\) is the geometric mean of \(XW\) and \(XY\).

$$ XZ^2 = XW \cdot XY $$

Solve for XZ

Substitute the known segment lengths.

$$ XZ^2 = 7 \cdot 28 = 196 $$

$$ XZ = \sqrt{196} = 14 $$

Answer:

Consider triangle \(XYZ\) with altitude \(WZ\). What is \(XZ\)?
\(XZ =\) <blank>14</blank>