Problema Solution
Bricks are delivered to a work site and stacked in rows and columns, forming a rectangular prism. The length of the prism is 1 foot greater than its width, and its height is 2 feet less than its width. Find the dimensions of the prism formed by the bricks, given that its volume is 40 cubic feet.
Answer provided by our tutors
let
x = the width of the prism, x>0
x + 1 = the length of the prism
x - 2 = the height of the prism
V = 40 ft^3 the volume of the prism
since V = width*length*height we have:
x(x + 1)(x - 2) = 40
x^3 - x^2 - 2x - 40 = 0
lets draw the graph of the function y = x^3 - x^2 - 2x - 40
click here to see the graph:
from the graph we see that the function has a zero for x = 4 (it is the intersection with the x-axis)
indeed if we plug x = 4 into the equation x(x + 1)(x - 2) = 40 we get 4(4 + 1)(4 - 2) = 40
the width is 4 ft
the length is 4 + 1 = 5 ft
the height is 4 - 2 = 2 ft