the perimeter of a rectangular field is 720 ft the length of the pool is four feet less than 3 times the width what are the dimensions

Answer 1

The perimeter of a rectangle is 2L + 2W where L is the length and W is the width. We are given that the length (L) is 4 ft. less than 3 times the width (W). Putting that algebraically, L = 3W - 4. Since we have an expression for the length in terms of the width, we can say that the perimeter is

2L + 2W = 2(3W - 4) + 2W

2L + 2W = 6W - 8 + 2W

2L + 2W = 6W + 2W - 8

2L + 2W = 8W - 8

2L + 2W = 8(W - 1)

Since the perimeter is expressed algebraically as 8(W - 1) and we are told that the perimeter is equal to 720 ft., the two quantities are equal and we have

8(W - 1) = 720 ft.

W - 1 = 90 ft.

W = 91 ft.

Thus, the width of the field is W = 91 ft. and the length of the field is L = 3W - 4 = 3(91) - 4 = 273 - 4 = 269 ft.