Question

two nearby trees are perpendicular to the ground, which is flat. one of these trees is 10 feet tall and has a shadow that is 5 feet long. at the same time, the shadow of the other tree is 2 feet long. how tall, in feet, is the other tree?
a 3
b 4
c 8
d 27

Explanation:

Step1: Set up proportion

Since the ratio of tree - height to shadow - length is the same for both trees, we can set up the proportion $\frac{h_1}{s_1}=\frac{h_2}{s_2}$. Let $h_1 = 10$ feet (height of the first tree), $s_1 = 5$ feet (shadow - length of the first tree), $s_2=2$ feet (shadow - length of the second tree), and $h_2$ be the height of the second tree we want to find. So, $\frac{10}{5}=\frac{h_2}{2}$.

Step2: Solve for $h_2$

Cross - multiply: $10\times2 = 5\times h_2$. Then $20 = 5h_2$. Divide both sides by 5: $h_2=\frac{20}{5}=4$.

Answer:

B. 4