## Elementary Algebra

$a=6\sqrt2$
Plugging in values into the Pythagorean Theorem gives: $a^2 +7^2 = 11^2$ Simplfy by subtracting $7^2$ from both sides, we find: $a^2 = 11^2-7^2 = 121-49 = 72$ To solve $a^2=72$, take the square root of both sides: $\sqrt a^2 = \sqrt 72 = 36\times 2$ Simplifying gives the answer: $a = 6\sqrt 2$