Question

A fence post that is 5 feet tall casts a 2-foot shadow at the same time that a tree that is 27 feet tall casts a shadow in the same direction. Determine the length of the tree's shadow.

A- 8.5 feet
B- 10.8 feet
C- 12 feet
D- 21.4 feet

Answer 1

Answer: B- 10.8 feet

Explanation:

We can create a proportion to solve. Let x be the length of the tree's shadow. I have drawn a figure to demonstrate what is happening, see the image attached. This picture is not drawn to scale.

Given:

`\displaystyle \frac{\text{Tree\;height}}{\text{Fence\;post\;height}} =\frac{\text{Tree\;shadow}}{\text{Fence\;post\;shadow}}`

Substitute knowns:

`\displaystyle (27)/(5) =(x)/(2)`

Cross-multiply:

5 * x = 27 * 2

5x = 54

Divide both sides of the equation by 5:

x = 10.8

The length of the tree's shadow is 10.8 feet (B).