SOLUTION: Tracy is trying to find the perfect shoe box for her brand new pair of high heeled shoes. She found a square-based shoe box whose height is 4 cm more than the side length of its s

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Tracy is trying to find the perfect shoe box for her brand new pair of high heeled shoes. She found a square-based shoe box whose height is 4 cm more than the side length of its s      Log On


   

Question 1005809: Tracy is trying to find the perfect shoe box for her brand new pair of high heeled shoes. She found a square-based shoe box whose height is 4 cm more than the side length of its square base. If the volume of the box is 225 cm3, what are its dimensions?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
h height
x each base dimension
volume is hx%5E2.
Given: h=x%2B4
volume is 225.

%28x%2B4%29x%5E2=225

x%5E3%2B4x%5E2-225=0

Several rational roots to try, such as plus&minus of 1,3,5,15,25,9. Be sure your first dividend for your synthetic divisions are x%5E3%2B4x%5E2%2B0%2Ax-225. The rest of doing this process is now back to you to continue.

You will find a root of 5 corresponding to (x-5) factor, and the resulting x%5E2%2B9x%2B45 as quadratic factor. The quadratic factor here has only complex roots with imaginary component.

highlight%28x=5%29 for a side of the square base.
------------and highlight%28h=9%29.