Question 101538: An ecology center wants to set up an experimental garden using 300 m of fencing to enclose a rectangular area of 5000 m^2. Find the dimensions of the garden.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Start with the basic formulas for perimeter and area:
1) P = 2(L+W) where L = Length and W = Width.
2) A = L*W
You are given that P = 300m and A = 5000 sq.m. so plug these values into the two equations thus:
1a) 300 = 2(L+W)
2a) 5000 = L*W
Now you have a system of equations with two unknowns.
Solve equation 1a) for L
1b) L = 150-W now substitute this into equation 2a) and solve for W.
2b) 5000 = (150-W)*W Simplify this.
W^2-150W+5000 = 0 This quadratic equation can be solved by factoring, so...
(W-100)(W-50) = 0
So W = 100 or W = 50
Now we need to find L and we can use equation 1b.
L = 150 - W and, if W = 50m, then:
L = 100m or, if W = 100m, then:
L = 50m.
The dimensions of the garden are: 100m by 50m
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