#### Answer

$a=6\sqrt 2$

#### Work Step by Step

According to the Pythagorean Theorem, if $a$ and $b$ are the lengths of the shorter sides of a right triangle and $c$ is the length of the longest side, then $a^{2}+b^{2}=c^{2}$.
Therefore, $a^{2}+7^{2}=11^{2}$.
$a^{2}+49=121$
Subtract 49 from both sides.
$a^{2}=72$
Take the square root of both sides.
$a=\sqrt 72=\sqrt (36\times2)=\sqrt 36\times\sqrt2=6\sqrt 2$