SOLUTION: A rectangular field, the length twice the width, is enclosed. If the fence posts were placed 16 ft. apart instead of 12 ft., 66 less posts would be needed. Determine number of ac

Question 1060259: A rectangular field, the length twice the width, is enclosed. If the fence posts were placed 16 ft. apart instead of 12 ft., 66 less posts would be needed. Determine number of acres in field.
Area = length * width
l = 2w
Not sure how to proceed. Thanks.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
length(l) = 2 * width(w)
:
l = 2w
:
Perimeter = 2(2w) + 2w = 6w
:
we are given two equations
:
1) 6w / 12 = n, where n is number of posts
:
2) 6w / 16 = n - 66
:
substitute 6w / 12 for n in equation 2
:
6w / 16 = (6w / 12) - 66
:
use 48 as common denominator, multiply both sides of = by 48
:
3 * 6w = (4 * 6w) - (66 * 48)
:
18w = 24w - 3168
:
6w = 3168
:
w = 528 feet
:
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Area(A) = (528 * 2) * 528 = 557,568 square feet
:
1 Acre = 43,560 square feet
:
A in acres = 557,568 / 42,560 = 13.1008
:
A in acres is approximately 13.1 acres
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