$3^{2}+4^{2}+12^{2}$ is equal to
(A) $13^{2}$
(B) $19^{2}$
(C) $17^{2}$
(D) $15^{2}$
(E) $11^{2}$
Solution 1

Calculating, $3^{2}+4^{2}+12^{2}=9+16+144=25+144=169=13^{2}$.

## Solution 2

From our work with the Pythagorean Theorem, we might remember that $3^{2}+4^{2}=5^{2}$.

(This comes from the " $3-4-5$ " right-angled triangle.)

Thus, $3^{2}+4^{2}+12^{2}=5^{2}+12^{2}$.

We might also remember, from the "5-12-13" triangle that $5^{2}+12^{2}=13^{2}$.

Therefore, $3^{2}+4^{2}+12^{2}=5^{2}+12^{2}=13^{2}$.

ANSWER: (A)