SOLUTION: A 1200 square foot rectangular garden is enclosed with 150 ft of fencing. Find the dimensions of the garden to two decimal places.

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Question 762657: A 1200 square foot rectangular garden is enclosed with 150 ft of fencing. Find the dimensions of the garden to two decimal places.
Answer by Stitch(470)   (Show Source): You can put this solution on YOUR website!
The equation for the area of a rectangle is A=L*W
The equation for the perimeter of a rectangle is P=2L+2W
Given: A=1200 & P=150
Equation 1:
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Start by solving equation 2 for one of the variables.
Equation 2:
Subtract 2L from both sides.

Factor out a 2 on the left side of the equation.

Divide both sides by 2.

Now plug (75-L) into equation 1 for W.
Equation 1:
Multiply the L through.

Subtract 1200 from both sides.

Now you can use the quadratic equation to solve for L.
Solved by pluggable solver: SOLVE quadratic equation with variable
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=825 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 23.1385933836549, 51.8614066163451. Here's your graph:

You will end up with two values for L.
L is equal to 23.14 & 51.86
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Using the values for L, solve for W.



or


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In other words the length and width can be switched but the dimensions have to be 23.14ft and 51.86ft

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