SOLUTION: The swinomish planning office has 300 feet of fencing and wants to enclose a rectangular area of 3600 square feet to protect a cultural site. What should the length and width of t

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Question 35452: The swinomish planning office has 300 feet of fencing and wants to enclose a rectangular area of 3600 square feet to protect a cultural site. What should the length and width of the fenced area be.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = width of the rectangle
y = length of the rectangle

Two equations are given in this problem:
Area = xy = 3600 square feet
Perimeter = 2x+2y = 300 feet

In the second equation, it will be easy to solve for y by dividing both sides by 2:
x+y = 150
y= 150-x

Substitute this back into the first equation:
xy+=+3600
x%28150-x%29+=+3600
150x+-+x%5E2+=+3600

This is a quadratic equation. Set the equation equal to zero, by adding %2Bx%5E2+-150x to each side of the equation.
0+=+x%5E2+-+150x+%2B3600

Does it factor??? Probably so!
0=%28x-30%29%28x-90%29
x=30 or x= 120

If x = 30, then y = 120, and if x= 120, then y = 30. It would be appropriate to say that the width would be the smaller number x= 30 feet, and the length is the larger number, which would be y = 120 feet.

R^2 at SCC