Question

Activity

Lewis directs the school marching band. He uses scale drawings of the football field to design marching formations for the band. The football field is 100 yards long and 53 1/3 yards wide. Lewis always uses a scale of 1 inch to 10 yards for his drawings.

Complete the steps below to find the length and width of the football field as it appears in one of Lewis’s scale drawings.

Part A
What is the actual area of the football field? Assume that the field is shaped like a rectangle.
Part B
Write a ratio to represent the scale used in the drawing.
Part C
What is the length of the football field in the scale drawing?
Part D
What is the width of the football field in the scale drawing?
Part E
What is the area of the football field in the scale drawing? Assume that the field is shaped like a rectangle.
Part F
What is the ratio of the area of the football field in the scale drawing to the area of the actual football field?

Answer 1

Part A: 5,333
`(1)/(3)` square yards

EX: The length of the football field is 100 yards. The width of the field is 53
`(1)/(3)` yards.

Part B: 1/10 inch per yard

EX: The scale used in the drawing is 1 inch to 10 yards. I can represent this ratio in several different ways: 1 inch to 10 yards, 1 inch : 10 yards, 1 in/ 10 yd or 1/10

Part C: 10 inches

EX: Set up a proportion where the numerators are the measurements in the scale drawing and the denominators are the actual measurements of the football field:

1 in. / 10 yd. = × in. / 100 yd.

Cross multiply, and then divide both sides by 10 to solve for x:

100 = 10x

10 = x

Part D: 5 1/3

EX: Use the actual width of 53
`(1)/(3)` yards and the scale to find the width of the field in the scale drawing.

Set up a proportion where the numerators are the measurements in the scale drawing and the denominators are the actual measurements of the football field:

1 in / 10 yd = 53
`(1)/(3)` yd

Cross multiply, and then divide both sides by 10 to solve for x:

10x = 53
`(1)/(3)`

x = 160/3 ÷ 10

x = 16/3

x = 5
`(1)/(3)`

Part E: 53 1/3

EX: In the scale drawing, the length of the football field is 10 inches and the width is 5
`(1)/(3)` inches. The area of a rectangle is length × width:

area = length × width

= 10 in. x 5
`(1)/(3)` in.

= 53
`(1)/(3)` sq. in. ( square inches)

Part F: The ratio is 1 square inch to 100 square yards

EX: The area of the football field in the scale drawing is 53
`(1)/(3)` square inches.

The area of the actual football field is 5,333
`(1)/(3)` square yards.

The calculation for the ratio of the scaled area to the actual area is

53
`(1)/(3)` sq. in. / 5,333
`(1)/(3)` sq. yd. = 1 sq. in. / 100 sq. yd.

Explanation: