Question

a utility pole is 16 yards tall and its shadow is 12 yards long. a nearby plum tree is 8 yards tall. how long is the plum trees shadow? write your answer as a whole number or a decimal. do not round. yards

Explanation:

Step1: Set up proportion

Let \(x\) be the length of the plum tree's shadow. Since the ratio of height to shadow length is the same for both objects, we have \(\frac{16}{12}=\frac{8}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(16x = 12\times8\).

Step3: Simplify the right - hand side

\(12\times8 = 96\), so the equation becomes \(16x=96\).

Step4: Solve for \(x\)

Divide both sides by \(16\): \(x=\frac{96}{16}\).

Answer:

\(6\)