Question

in right triangle prt, m∠p=90°, altitude pq drawn to hypotenuse rt, rt=17, and pr=15
determine and state, to the nearest tenth, the length of pq.

Explanation:

Step1: Identify similar triangles

In right triangle $PRT$ with altitude $PQ$ to hypotenuse $RT$, $\triangle PRQ \sim \triangle TRP$.

Step2: Set up proportion

Corresponding sides of similar triangles are proportional: $\frac{RQ}{PR} = \frac{PR}{RT}$

Step3: Substitute known values

$PR=15$, $RT=17$, so:
$\frac{RQ}{15} = \frac{15}{17}$

Step4: Solve for $RQ$

Multiply both sides by 15:
$RQ = \frac{15^2}{17} = \frac{225}{17} \approx 13.2$

Answer:

The length of $RQ$ is approximately $\boldsymbol{13.2}$