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 $PRT$ with altitude $PQ$ to hypotenuse $RT$, $\triangle PRT \sim \triangle QRP$. This means corresponding sides are proportional: $\frac{PR}{RT} = \frac{RQ}{PR}$.

Step2: Rearrange to solve for $RQ$

Isolate $RQ$ by cross-multiplying: $RQ = \frac{PR^2}{RT}$

Step3: Substitute given values

Substitute $PR=15$, $RT=17$:
$RQ = \frac{15^2}{17} = \frac{225}{17}$

Step4: Calculate and round

Compute the value and round to the nearest tenth:
$\frac{225}{17} \approx 13.2$

Answer:

13.2