Question

estelle found that a plum tree that is 12 feet tall casts a shadow 16 feet long. then estelle noticed a nearby stop sign that is 9 feet tall. how long is the stop signs shadow? write your answer as a whole number or a decimal. do not round. feet

Explanation:

Step1: Set up the proportion

Since the height and shadow length are proportional, we have $\frac{\text{tree height}}{\text{tree shadow}}=\frac{\text{stop - sign height}}{\text{stop - sign shadow}}$. Let $x$ be the length of the stop - sign's shadow. So, $\frac{12}{16}=\frac{9}{x}$.

Step2: Cross - multiply

Cross - multiplying gives $12x = 16\times9$.

Step3: Solve for $x$

First, calculate $16\times9 = 144$. Then, $12x=144$. Divide both sides by 12: $x=\frac{144}{12}$.

Answer:

12