SOLUTION: The perimeter of a rectangle is 60 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 144 square feet.

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Question 293223: The perimeter of a rectangle is 60 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 144 square feet.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width = x
Let the length = y
Let the perimeter = P
Let the area = A
P+=+60
60+=+2x+%2B+2y
2y+=+60+-+2x
y+=+30+-+x
A+=+x%2A%2830+-+x%29
A+=+-x%5E2+%2B+30x
It is given that A+%3C=144 ft2
144+=+-x%5E2+%2B+30x
144+=+x%2A%28-x+%2B+30%29
I'll take a guess x+=+10
144+=+10%2A%28-10+%2B+30%29
144+=+200
I'll try x+=+8
144+=+8%2A%28-8+%2B+30%29
144+=+8%2A22
144+=+176
I'll try x+=+6
144+=+6%2A%28-6+%2B+30%29
144+=+6%2A24
144+=+144 OK
Next,
x+=+4
144+=+4%2A%28-4+%2B+30%29
144+=+104
I deduce that x+%3C=6
and
y+%3E=+24
Either side must be less than or equal to 6
or greater than or equal to 24