A football coach uses a whiteboard that shows a scale diagram of the football field to plan plays in a game. In the diagram, the field is 354 cm long. The scale statement for the length of a football field is 1:33. How long is the actual football field?
a. 112.7 m
b. 130 m
(c. 116.8 m
d. 106.5 m
To find the length of the actual football field, we can multiply the length of the diagram by the scale factor.
Scale factor = actual length / diagram length
1:33 = actual length / 354 cm
To find the length in meters, we need to convert 354 cm to meters by dividing it by 100.
1:33 = actual length / (354 cm / 100 cm/m)
1:33 = actual length / 3.54 m
To isolate the actual length, we can cross multiply:
1 * 3.54 m = 33 * actual length
3.54 m = 33 * actual length
Dividing both sides of the equation by 33, we get:
actual length = 3.54 m / 33
actual length ≈ 0.1073 m
Therefore, the length of the actual football field is approximately 106.5 m.
The correct answer is d. 106.5 m.