Question

question 14 of 25 which expression gives the length of $overline{qr}$ in the triangle shown below? a. $17^{2}+25^{2}$ b. $17 + 25$ c. $sqrt{17 + 25}$ d. $sqrt{17^{2}+25^{2}}$

Explanation:

Step1: Identify right - triangle and Pythagorean theorem

In right - triangle $QRS$ with right - angle at $S$, by the Pythagorean theorem, for a right - triangle with legs $a$ and $b$ and hypotenuse $c$, $c^{2}=a^{2}+b^{2}$. Here, the legs are $RS = 17$ and $QS=25$, and $QR$ is the hypotenuse.

Step2: Apply the Pythagorean theorem

If $a = 17$ and $b = 25$, and $QR=c$, then $c=\sqrt{a^{2}+b^{2}}=\sqrt{17^{2}+25^{2}}$.

Answer:

D. $\sqrt{17^{2}+25^{2}}$