Question

Reagan Nichols wanted to create a running path around the rectangular soccer field so she could also train for cross-country. If the dimensions of the total area are 180 meters by 75 meters, what are the dimensions of the soccer field if the area of soccer field is equal to the area of the running path?

a) What are the dimensions of the soccer field?

60 meters by 75 meters
180 meters by 75 meters
75 meters by 60 meters
180 meters by 60 meters

Answer 1

To find the dimensions of the soccer field, whose area is equal to the running path around it, we can solve the equation where the total area's width is reduced by twice the width of the path on each side.

Step-by-step explanation:

The student is asking to determine the dimensions of the soccer field if the area of the soccer field is equal to the area of the running path around it. The total area including both is given as 180 meters by 75 meters. To solve this problem, we can assume that the width of the running path around the soccer field is 'x' meters. Thus, the dimensions of the soccer field would be (180 - 2x) meters by (75 - 2x) meters. Since the area of the running path is equal to the area of the soccer field, we can set up the equation:

(180 meters * 75 meters) / 2 = (180 - 2x) meters * (75 - 2x) meters.

After solving this equation, we would get the value of 'x' and subsequently the dimensions of the soccer field.