Question

A box company is designing a new rectangular gift container. The marketing department has designed a box with a width 2 inches shorter than its length and a height 3 inches taller than its length. The volume of the box must be 56 cubic inches. What are the dimensions of the box?
The width is ? .......? inches,

the length is ?..........? inches and the

height is ?........? inches.

Answer 1

Volume of the box= 56 cubic inches
let x is the length, then
width =2 inches shorter than its length = x - 2
height =  3 inches taller than its length = x+3
Volume = length x width x height
56 = x x (x-2) x (x+3)
56 = (x² -2x)(x+3)
56 = x³ +3x² -2x² - 6x
56 = x³ + x² -6x
x³+x²-6x-56 = 0
using the rational root theorem and factoring the polynomial;
(x-4)(x² +5x +14) = 0
from here;
x-4 = 0
x = 4
So, length = 4 inches
width = x - 2 = 4 -2 = 2 inches
length = x + 3 = 4 + 3 = 7 inches
volume = l x w x h = 4 x 2 x 7 = 56