## Algebra 1

In the equation $a^2+b^2=c^2$, a and b are the lengths of the two legs and c is the length of the hypotenuse. $a^2+b^2=c^2\longrightarrow$ substitute the given values $12^2+x^2=13^3\longrightarrow$ compute the squares $144+x^2=169\longrightarrow$ subtract 144 from each side $144+x^2-144=169-144\longrightarrow$ subtract $x^2=25\longrightarrow$ find the square root of each side $\sqrt {x^2}=\sqrt {25}\longrightarrow$ simplify $x=5$