algebra word problem

Question

A box in the shape of a rectangular prism has a volume of 96 cubic feet. The box has a length of (x+8)(x+8) feet, a width of xx feet, and a height of (x−2)(x−2) feet. Find the dimensions of the box.

Answer 1

Hey! Lets solve this shall we ? So, we must find the dimension of the length, width and height us the Volume of a Rectangular Prism formula such that

V = l*w*h. Then, we plug in our information to obtain the dimensions such that

96 = (x + 8) * x * (x - 2).......We then multiply the binomials together; leaving x out to get

96 = x * (x^2 + 8x - 2x - 16)......Then we add like terms such that

96 = x * (x^2 + 6x - 16).........Then we distribute the x inside to ge t

96 = x^3 + 6x^2 - 16x..........Then we subtract 96 to the right side to get

0 = x^3 + 6x^2 - 16x - 96..........Then we factor by grouping

0 = x^2 * (x + 6) - 16 * (x + 6)..........Then factor (x+6)

0 = (x^2 - 16) * (x + 6)..........Then continue factoring

0 = (x - 4) * (x + 4) * (x + 6).......Use the Zero-Product Property of Equality and solve for x such that

x = -6 , -4 , 4

x = -6 and x = -4 are erroneous because we cannot have a negative foot in measurement so we use

x = 4. Then we plug this value into the three dimensions to get

x + 8 = 4 + 8 = 12

x - 2 = 4 - 2 = 2

Length = 12

Width = 4

Height = 2

I hope this helped!