What is the height and width of a box of the volume is 768 cubic inches and the area is 448 square inches?

Question

An open box (with no lid) has a square base and four sides of equal height. The height is 4 greater than the length abs width. What are the dimensions of the box if the volume is 768 cubic inches and the surface area is 448 square inches?

Answer 1

x=a side of the square base

x+4=height of the box

surface area is the area of the square base and the areas of the 4 rectangular sides added together

x^2 is the area of the square base

x(x+4) is the area of one of the rectangular sides, of which there are 4

x^2+4*x(x+4)=448

x^2+4x^2+16x=448

5x^2+16x-448=0

5*448=5*2*2*2*2*2*2*7=(5*2*2*2)*(2*2*2*7)=40*56 and 56-40=16

factor

(5x+56)(x-8)=0

x-8=0

x=8 inches

the square base is 8 inches by 8 inches and the height is 8+4=12 inches

check:

volume=8*8*12=8*96=768 cubic inches

surface area=8^2+4*8*12=64+384=448 square inches