SOLUTION: The perimeter of a rectangle is 52 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 120 square feet

Question 358647: The perimeter of a rectangle is 52 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 120 square feet
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
2x+2y=52
xy=120 or x=120/y
2(120/y)+2y=52
240/y+2y=52
(240+2y*y)/y=52
(240+2y^2)/y=52 cross multiply.
2y^2+240=52y
2y^2-52y+240=0
2(y^2-26y+120)=0
2(y-20)(y-6)=0
y-20=0
y=20 ans.
x=120/20=6 ans.
y-6=0
y=6 ans.
x=120/6=20 ans.
Proof:
20*6=120 ans. area.
2*20+2*6=40+12=52 ans. perimeter.
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