## Thinking Mathematically (6th Edition)

$x=3.75$ ft
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: $12x=5(9) \\12x=45 \\x = \frac{45}{12} \\x=3.75$