Question

Derek wants to determine the height of the top of the backboard on the basketball goal at the playground. He places a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 10 inches and the backboard has a shadow of 8.5 feet, then how high is the top of the backboard?

Answer 1

Answer:

10.2 feet.

Step-by-step explanation:

We have been given that Derek places  a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 10 inches. We are asked t find the height of the backboard, if the backboard has a shadow of 8.5 feet.

We will use proportions to solve our given problem as ratio between sides ruler will be equal to ratio of sides of background.

$\frac{\text{Actual height of ruler}}{\text{Shadow of ruler}}=\frac{\text{Actual height of backboard}}{\text{Shadow of backboard}}$

$\frac{12}{10}=\frac{\text{Actual height of backboard}}{8.5}$

$\frac{12}{10}*8.5=\frac{\text{Actual height of backboard}}{8.5}*8.5$

$1.2*8.5=\text{Actual height of backboard}$

$10.2=\text{Actual height of backboard}$

Therefore, the actual height of the back-board is 10.2 feet.