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

Algebra ->  Rectangles -> 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      Log On


   

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) About Me  (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