Question

in right triangle prt, $m\angle p=90^{\circ}$, altitude pq drawn to hypotenuse rt, rt=17, and pr=15
determine and state, to the nearest tenth, the length of rq.

Explanation:

Step1: Identify similar triangles

In right triangle $PRT$, altitude $PQ$ to hypotenuse $RT$ creates similar triangles $\triangle PRT \sim \triangle QRP$.

Step2: Set up proportion

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

Step3: Substitute known values

$PR=15$, $RT=17$. Substitute into proportion:
$\frac{15}{17} = \frac{RQ}{15}$

Step4: Solve for $RQ$

Rearrange to isolate $RQ$:
$RQ = \frac{15^2}{17} = \frac{225}{17}$

Step5: Calculate decimal value

Compute and round to nearest tenth:
$RQ \approx 13.2$

Answer:

$13.2$