Question

in the following triangle, find length ( kl ). round to the nearest tenth.

Explanation:

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

In a right - triangle \( \triangle PKR\) with right - angle at \(K\) and altitude \(KL\) to the hypotenuse \(PR\), the formula is \(KL=\sqrt{PL\times LR}\).

Step2: Substitute the given values

Given \(PL = 7.5\) and \(LR=11.7\). Then \(KL=\sqrt{7.5\times11.7}\).
First, calculate \(7.5\times11.7 = 87.75\).
Then, \(KL=\sqrt{87.75}\approx9.4\).

Answer:

\(9.4\)