find dimensions of the original piece of cardboard?

Question

construction..an open topped rectangular box is formed by cutting a 6-inch square from each corner of a rectangular piece of cardboard and bending up the ends and sides.the area of the cardboard before the corners are removed is 768 square inches and the volume of the box is 1440 cubic inches.find the dimensions of the original piece of cardboard.

Answer 1

6xy = 1440

xy = 240

 

(x + 12)(y + 12) = 768

xy + 12x + 12y + 144 = 768

240 + 12x + 12y + 144 = 768

384 + 12x + 12y = 768

12x + 12y = 384(

x + y = 32

 

x(32- x) = 240

32x - x² = 240

0 = x² - 32 + 240

0 = (x - 12)(x - 20)

 

Original sheet was 32 x 24