Question

a utility pole is 40 feet tall. close by, there is an oak tree that is 64 feet tall. if the utility poles shadow is 19.5 feet long, how long is the oak trees shadow? write your answer as a whole number or a decimal. do not round. feet

Explanation:

Step1: Set up the proportion

Since the height of an object and the length of its shadow are proportional at the same time and place. Let \(x\) be the length of the oak tree's shadow. The proportion is \(\frac{\text{height of utility pole}}{\text{length of utility pole's shadow}}=\frac{\text{height of oak tree}}{\text{length of oak tree's shadow}}\), i.e., \(\frac{40}{19.5}=\frac{64}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(40x = 19.5\times64\).

Step3: Solve for \(x\)

First, calculate \(19.5\times64 = 1248\). Then \(x=\frac{1248}{40}=31.2\).

Answer:

\(31.2\)