SOLUTION: The area of a rectangular piece of cardboard shown is 735 square inches. The cardboard is used to make an open box by cutting a 3-inch square from each corner and turning up the s

Question 205186: The area of a rectangular piece of cardboard shown is 735 square inches. The cardboard is used to make an open box by cutting a 3-inch square from each corner and turning up the sides. If the box is to have a volume of 1305 cubic inches, find the dimensions of the cardboard that must be used. Any help you can give would be greatly appreciated, thanks!!
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
xy=735
x=735/y
(x-2*3)(y-2*3)*3=1305
(735/y-6)(y-6)*3=1305
(735-6y-6*735/y+36)*3=1305
(735-6y-4410/y+36)*3=1305
2205-18y-13230/y+108=1305
-18y-13230/y=1305-2205-108
-18y-13230/y=-1008
(-18y*y-13230)/y=-1008
-18y^2-13230=-1008y
18y^2-1008y+13230=0
18(y^2-56y+735)=0
18(y-21)(y-35)=0
y-21=0
y=21 then x=35
y-35=0
y=35 then x=21
Proof:
21*35=735
735=735
(21-2*3)(35-2*3)*3=1305
(21-6)(35-6)*3=1305
15*29*3=1305
1305=1305
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