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?
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
