SOLUTION: A rectangular piece of cardboard is to be formed into an uncovered box. The piece of cardboard is 2 cm longer than it is wide. A square that measures 3 cm on a side is cut from eac

Question 135987: A rectangular piece of cardboard is to be formed into an uncovered box. The piece of cardboard is 2 cm longer than it is wide. A square that measures 3 cm on a side is cut from each corner. When the sides are turned up to form a box, its volume is 765 cubic cm. Find the dimensions in cm of the original piece of cardboard.
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
LENGTH=X+2
WIDTH=X
AFTER CUTING THE 3CM SQUARE OUT OF THE CORNERS WE HAVE THE LENGTH=(X+2-6)
WIDTH=(X-6)
HEIGHT=3
765=3(X-6)(X+2-6)
765=(3X-18)(X-4)
765=3X^2-18X-12X+72
3X^2-30X+72-765=0
3X^2-30X-693=0
3(X^2-10X-231)=0
(X-21)(X+11)=0
X-21=0
X=21 ANSWER FOR THWE WIDTH.
21+2=23 ANSWER FOR THE LENGTH.
PROOF
3(21-6)(23-6)=765
3*15*17=765
765=765

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