The perimeter of a rectangular field is P feet. The width ofthe field is 200 less than its length. In terms of P, what is thelength of the field in feet?
Question
The perimeter of a rectangular field is P feet.
The width of the field is 200 less than its length.
In terms of P, what is the length of the field in feet?
Solution
The perimeter of a rectangle is given by the formula P = 2L + 2W, where L is the length and W is the width.
According to the problem, the width of the field is 200 less than its length. So, we can express the width as W = L - 200.
Substitute W = L - 200 into the perimeter formula:
P = 2L + 2(L - 200) P = 2L + 2L - 400 P = 4L - 400
To solve for L, add 400 to both sides and then divide by 4:
L = (P + 400) / 4
So, the length of the field in terms of P is (P + 400) / 4 feet.
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