State what the length of the other leg is in a right triangle whose hypotenuse is 13 and one leg is 12 by using the Pythagorean Theorem.

Question

anonymous · Answer

6?

kinggeorge · Answer

6 Is not correct. The pythagorean theorem says that $$c=\sqrt{a^2+b^2}$$correct?

anonymous · Answer

Yes. I tried that and it doesn't come up with any of the multiple choice answers.

kinggeorge · Answer

Let's rearrange it to find $a$.$$\begin{aligned}
c&=\sqrt{a^2+b^2}\
c^2&=a^2+b^2\
c^2-b^2&=a^2\
\sqrt{c^2-b^2}&=a
\end{aligned}$$

kinggeorge · Answer

Now plug in $13=c$, and $12=b$. We get $$\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}$$So what's $\sqrt{25}$?

anonymous · Answer

Is it simplified to 5? And the other leg.

kinggeorge · Answer

Right. So the length of your third leg must be 5.

anonymous · Answer

Thanks for the help.

kinggeorge · Answer

No problem.