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?
its 10.8
its 9.82
To determine the height of the top of the backboard, we can use the concept of similar triangles.
First, let's convert the shadow of the backboard from feet to inches. Since 1 foot is equal to 12 inches, the shadow of 8.5 feet can be converted to 8.5 x 12 = 102 inches.
Now we have the following measurements:
Shadow of the ruler = 10 inches
Shadow of the backboard = 102 inches
Since the triangles formed by the ruler and the backboard are similar, their corresponding sides are proportional.
Let h represent the height of the top of the backboard.
Therefore, we can set up the following proportion based on their corresponding sides:
10 inches / 102 inches = 12 inches / h
To solve for h, we can cross-multiply and divide:
10 inches * h = 102 inches * 12 inches
10h = 1224 inches
Dividing both sides of the equation by 10:
h = 1224 inches / 10
h = 122.4 inches
Therefore, the height of the top of the backboard is 122.4 inches.
x=8.18
Cross multiply and solve for x
12/10 = x/8.5