Question

question
a tree casts a 38 foot shadow at the same time a boy casts a 9 foot shadow. if the boy is 5.5 feet tall, how tall is the tree?
interpret the answer.
select the correct answer below:
a 38 foot tall tree casts a 23.2 foot shadow.
a 5.5 foot tall boy casts a 23.2 foot shadow.
a 23.2 foot tall tree casts a 9 foot shadow.
a 23.2 foot tall tree casts a 38 foot shadow.

Explanation:

Step1: Set up proportion

Let \( h \) be the height of the tree. Using the proportion \(\frac{\text{height of object}}{\text{length of shadow}}\), we have \(\frac{h}{38}=\frac{5.5}{9}\).

Step2: Solve for \( h \)

Cross - multiply: \( 9h = 5.5\times38\). Then \(h=\frac{5.5\times38}{9}\). Calculate \(5.5\times38 = 209\), so \(h=\frac{209}{9}\approx23.2\).

Answer:

D. A 23.2 foot tall tree casts a 38 - foot shadow.