helpp me with scale factor

Question

on a blueprint, the area of a basketball court is 58 square inches. 

 

A. If the scale on the blueprint is 1 inch : 9 feet, what is the actual area of the basketball court? 

B. If the length of the basketball court on the blueprint is 10.4 inches, what is the actual length of the basketball court?

C. what is the actual width of the basketball court to the nearest foot?

Answer 1

1. First convert your scale into the units you need, which is square inches to square footage. You can accomplish that by squaring your scale in this way:  (1 inch : 9 feet)^2 = 1 square inch : 81 square feet (this is now your new scale for conversion)

if 1 square inch is 81 square feet, you can simply multiply 58 square inches (the area of the basketball court) by 81.

58x 81 = 4698 square feet.

2. This statement tells you that one side (the length) of the basketball court is 10.4 inches. Simply multiple 10.4 by your conversion (9 feet) to get the "actual length" of the basketball court. (10.4 x 9 = 93.6 feet)

3. Now that you know the length of the basketball court, you can use the answers from parts 1 and 2 to answer this.

Length = 93.6 feet

Area = 4698 square feet.

Width = ?

We know that a basketball court is a rectangular shape, so this implies that we will use the formula for calculating rectangular areas (Area = length x width)

4,698 square feet = 93.6 feet x width

If you divide both sides by 93.6 feet (4698/93.6 = 93.6 x width/93.6) You can isolate the width variable on one side, leaving you with 4698/93.6 = width

The width should be approx 50.2 (to the nearest foot is 50 feet)

 

Hope this helps!