For this problem a and b represent the lengths of the legs of a right triangle, and c represents the length of the hypotenuse. Find c if a = 10 centimeters and b = 15 centimeters. Express the answer in simplest radical form.
A) $\sqrt { 25 }$ centimeters
B) 25 centimeters
C) $5 \sqrt { 13 }$ centimeters
D) $5 \sqrt { 5 }$ centimeters

Question

Quizplus · Accepted Answer

Using the Pythagorean theorem, we have:

\begin{align*}
c^2 &= a^2 + b^2 \
&= 10^2 + 15^2 \
&= 100 + 225 \
&= 325 \
\end{align*}

Taking the square root of both sides, we get:

$$c = \sqrt{325} = \sqrt{5 \cdot 5 \cdot 13} = 5\sqrt{13}$$

Therefore, the answer is choice C.

For This Problem a and B Represent the Lengths of the Legs