Question

which expression gives the length of \\(\overline{qr}\\) in the triangle shown below? \\(\bigcirc\\) a. \\(\sqrt{17 + 25}\\) \\(\bigcirc\\) b. \\(17 + 25\\) \\(\bigcirc\\) c. \\(17^2 + 25^2\\) \\(\bigcirc\\) d. \\(\sqrt{17^2 + 25^2}\\)

Explanation:

Step1: Identify right triangle sides

In right $\triangle QSR$, right-angled at $S$:
Leg 1: $QS = 25$, Leg 2: $SR = 17$, Hypotenuse: $QR$

Step2: Apply Pythagorean theorem

Pythagorean theorem: $\text{Hypotenuse} = \sqrt{(\text{Leg}_1)^2 + (\text{Leg}_2)^2}$
Substitute values: $QR = \sqrt{25^2 + 17^2}$

Answer:

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