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 triangle type

The triangle is a right - triangle with legs 17 and 25, and we want to find the hypotenuse $QR$.

Step2: Apply Pythagorean theorem

For a right - triangle with legs $a$ and $b$ and hypotenuse $c$, the Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$. Here $a = 17$ and $b = 25$, so $QR=\sqrt{17^{2}+25^{2}}$.

Answer:

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