Now that we know that the altitude of a right triangle is the geometric mean of the hypotenuse segments, we can use that property to solve problems.

Problem 1

Given: ΔPQR; QD ⊥ PR; PD = 3; DR = 15. Find QD.

Step 1: Label the parts of the figure by dragging the measures on the right to the appropriate segments.

Step 2: Set up a proportion using the geometric mean from the figure.

hypotenuse segment 1 altitude = altitude hypotenuse segment 2

Drag the appropriate measures from the figure into the blank proportion shown below.

Step 3: Solve the proportion.

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Check Your Answer

The length of the altitude, x, is equal to √45, or approximately 6.71.