SOLUTION: Find the dimensions of a rectangular lawn whose perimeter is 100 feet and whose area is 600 square feet. --They want me to use the quadratic formula, but I don't know how to set

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Question 300563: Find the dimensions of a rectangular lawn whose perimeter is 100 feet and whose area is 600 square feet.
--They want me to use the quadratic formula, but I don't know how to set the equation up. That's all I'm having trouble with. I know how to use the quadratic formula fairly well. Can you please help me?
~Thanks!
Found 2 solutions by nerdybill, dabanfield:
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
Find the dimensions of a rectangular lawn whose perimeter is 100 feet and whose area is 600 square feet.
.
Let x = length
and y = width
.
2(x+y) = 100 (equation 1)
xy = 600 (equation 2)
.
Solve equation 2 for y:
xy = 600
y = 600/x
.
Substitute the above into equation 1 and solve for x:
2(x+y) = 100
2(x+600/x) = 100
x+600/x = 50
x^2+600 = 50x
x^2-50x+600 = 0
(x-20)(x-30) = 0
.
x = {20,30}
.
Dimensions are 20 feet by 30 feet

Answer by dabanfield(803) (Show Source):
You can put this solution on YOUR website!
Find the dimensions of a rectangular lawn whose perimeter is 100 feet and whose area is 600 square feet.
--They want me to use the quadratic formula, but I don't know how to set the equation up. That's all I'm having trouble with. I know how to use the quadratic formula fairly well. Can you please help me?
~Thanks!
Let W be the width and L the lenght of the rectangle. Then we have:
1.a) perimeter = 2*W + 2*L or
1.b) 100 = 2*W + 2*L
2.a) area = L*W or
2.b) 600 = L*W
From 2.b) we have L = 600/W
Substituting 600/W for L in equation 1.b we have:
100 = 2*W + 2*(600/W)
100 = 2*W + 1200/W
Multiply both sides of the equation above by W:
100*W = 2*W*W + 1200*(W/W)
100W = 2W^2 + 1200*1
2W^2 - 100W + 1200 = 0
Now you can use the quadratic formula to find W (remember dimensions are non-negative) then calculate L = 600/W.