Question

which expression gives the length of $overline{pq}$ in the triangle shown below? p 15 r 19 q a. 15 + 19 b. $sqrt{15 + 19}$ c. 15$^{2}$ + 19$^{2}$ d. $sqrt{15^{2}+19^{2}}$

Explanation:

Step1: Identify the triangle type

The triangle $\triangle PRQ$ is a right - triangle with right - angle at $R$, where $PR = 15$ and $RQ=19$.

Step2: Apply the Pythagorean theorem

For a right - triangle with legs $a$ and $b$ and hypotenuse $c$, the Pythagorean theorem is $c^{2}=a^{2}+b^{2}$. Here, if $a = 15$ and $b = 19$, and $PQ$ is the hypotenuse, then $PQ=\sqrt{15^{2}+19^{2}}$.

Answer:

D. $\sqrt{15^{2}+19^{2}}$