Answer
$13 \text{ } ft$
Work Step by Step
Let $x$ be the length of the ladder. Using $a^2+b^2=c^2$ or the Pythagorean Theorem, the conditions of the problem translate to
\begin{array}{l}\require{cancel}
5^2+12^2=x^2
.\end{array}
The equation above simplifies to
\begin{array}{l}\require{cancel}
25+144=x^2
\\
169=x^2
.\end{array}
Taking the square root of both sides, the equation above is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{169}=x
\\
x=13
.\end{array}
Hence, the length of the ladder, $x,$ is $
13 \text{ } ft
.$
