SOLUTION: Do you think you could help me with this? 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 gre

Algebra ->  Conversion and Units of Measurement -> SOLUTION: Do you think you could help me with this? 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 gre      Log On


   

Question 712235: Do you think you could help me with this?
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. Show how to find the dimensions of the prism formed by the bricks, given that its volume is 40 cubic feet.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The unknown being referenced is the width.

Let w be width
Length is w+1
Height is w-2

w%28w%2B1%29%28w-2%29=40

Some steps,
w%28w%5E2%2Bw-2w-2%29-40=0
w(w^2-w-2)-40=0
w%5E3-w%5E2-2w-40=0

Solving that is faster if you know synthetic division. You would use the idea of the Rational Roots Theorem to find values for w to satisfy the cubic equation. I'd suggest first working with +/-4, +/-5, +/-8, +/-10. When you get just one first root, the next two will be easy.

Some further work:
Good News! I tried some long divisions and found +5 or -5 are not roots, but that +4 is a root. One of the binomials is (w-4). The quotient from this was w%5E2%2B3w%2B10. So this means your polynomial equation is
%28w-4%29%28w%5E2%2B3w%2B10%29=0, so the quadratic part should be much easier to manage.
NOTE: The discriminant for that quadratic is -31, so the solution will contain an imaginary part. The only reasonable value for w is 4.