Question

Mr. Halling and Mr. Clair were asked to help design a new

football field for Marist College. Mrs. Kessler said that the
width of the field needs to be 12 yards less than the length. Find
the area and perimeter of the field in terms of x.

How do I solve?

Answer 1

Mrs. Kessler's statement: the width of the field is 12 yards less than the length, so the width can be represented as (x - 12) yards.

To find the area of the field, we can use the formula for the area of a rectangle, which is LENGHT TIMES WIDTH. In this case, the length is x yards and the width is (x - 12) yards, so the area is:

Area = length x width
Area = x(x - 12)
Area = x^2 - 12x

To find the perimeter of the field, we can use the formula for the perimeter of a rectangle, which is 2 times the length plus 2 times the width. In this case, the length is x yards and the width is (x - 12) yards, so the perimeter is:

Perimeter = 2(length + width)
Perimeter = 2(x + x - 12)
Perimeter = 2(2x - 12)
Perimeter = 4x - 24

Therefore, the area of the field in terms of x is x^2 - 12x, and the perimeter of the field in terms of x is 4x - 24.