Question

a birch tree is 9 meters tall. close by, there is a sailboat mast that is 12 meters tall. if the birch trees shadow is 12 meters long, how long is the sailboat masts shadow? write your answer as a whole number or a decimal. do not round. meters

Explanation:

Step1: Set up the proportion

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

Step2: Cross - multiply

Cross - multiplying gives $9x = 12\times12$.

Step3: Solve for $x$

$9x=144$, then $x=\frac{144}{9}$.

Answer:

$16$