Answer
$x=3.75$ ft
Work Step by Step
Similar triangles have corresponding sides that are proportional.
Use proportions to obtain:
$\begin{array}{ccc}
&\dfrac{\text{base of bigger triangle}}{\text{base of smaller triangle}} &= &\dfrac{\text{height of the bigger triangle}}{\text{height of the smaller triangle}}
\\&\dfrac{5+7}{5} &= &\dfrac{9}{x}
\\&\dfrac{12}{5} &= &\dfrac{9}{x}
\end{array}$
Cross-multiply to obtain:
$12x=5(9)
\\12x=45
\\x = \frac{45}{12}
\\x=3.75$
