Question

allison is 5 ft tall. one afternoon her shadow measured 2.5 ft. at the same time, the shadow of her favorite tree was 14.5 ft. what is the height of the tree?
a. 7.25 ft
b. 12.5 ft
c. 17 ft
d. 29 ft

Explanation:

Step1: Set up proportion

Since the ratio of height to shadow length is the same for Allison and the tree, we can set up the proportion $\frac{\text{Allison's height}}{\text{Allison's shadow length}}=\frac{\text{Tree's height}}{\text{Tree's shadow length}}$. Let the height of the tree be $x$. So $\frac{5}{2.5}=\frac{x}{14.5}$.

Step2: Cross - multiply

Cross - multiplying gives us $2.5x = 5\times14.5$.

Step3: Solve for $x$

First, calculate $5\times14.5 = 72.5$. Then $x=\frac{72.5}{2.5}=29$.

Answer:

D. 29 ft