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 a if $c = 14$ and $b = 5$ inches. Express the answer in simplest radical form.
A) $\sqrt { 221 }$ inches
B) $- \sqrt { 221 }$ inches
C) $- 3 \sqrt { 19 }$ inches
D) $3 \sqrt { 19 }$ inches

Question

Quizplus · Accepted Answer

We can use the Pythagorean theorem to find a:

\begin{align*}
a^2 + 5^2 &= 14^2 \
a^2 &= 196 - 25 \
a^2 &= 171 \
a &= \sqrt{171} \
a &= \sqrt{9\cdot19} \
a &= 3\sqrt{19}
\end{align*}

Therefore, the answer is D, $3\sqrt{19}$ inches.

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