Question 1058539: Researchers at a university need a 10,000 square meter rectangular plot on which to grow three hybrids of corn. The plot is to be enclosed by fencing and divided into three equal subplots by a pair of fences both parallel to the same pair of sides of rectangle. If 600 meters of fencing are to be used for the project, what are the dimensions of the plot? Thank you!
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
Researchers at a university need a 10,000 square meter rectangular plot on which to grow three hybrids of corn.
The plot is to be enclosed by fencing and divided into three equal subplots by a pair of fences both parallel to the same pair
of sides of rectangle. If 600 meters of fencing are to be used for the project, what are the dimensions of the plot? Thank you!
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I think that the problem is about the "lot", not the "plot".
With this change I will solve it below.
Let x be that dimension of the rectangular lot which is parallel to an additional pair of fences.
Let y be another dimension.
Then you have these two equations
xy = 10000, (1)
4x + 2y = 600. (2)
From (2), expess y = 300 - 2x and substitute it into (1). You will get
x*(300-2x) = 10000.
Solve this quadratic equation by any way you can.
Answer. x = 50, y = 200.
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