SOLUTION: find the dimensions of a rectangular garden that has a perimeter 100 ft and area 300 ft squared.

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Question 637860: find the dimensions of a rectangular garden that has a perimeter 100 ft and area 300 ft squared.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
find the dimensions of a rectangular garden that has a perimeter 100 ft and area 300 ft squared.
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P = 2L + 2W = 100
L + W = 50
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L*W = 300
L*(50-L) = 300
L^2 - 50L + 300 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1300 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 43.0277563773199, 6.97224362268005. Here's your graph:

L = x
L = 25 + 5sqrt(13) ft
W = 25 - 5sqrt(13) ft
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