SOLUTION: the width of a box is 4 inches more thm the height. the length is the difference of 9 inches and the height. the volume of the box is 180 cubic inches. what are all the possible di

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Question 1081491: the width of a box is 4 inches more thm the height. the length is the difference of 9 inches and the height. the volume of the box is 180 cubic inches. what are all the possible dimensions for the box?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
w width
h height
L length
system%28w=h%2B4%2CL=h-9%2CwhL=180%29

First two equations formulas in terms of h.
system%28w=h%2B4%2CL=h-9%29

Substitute into the volume equation:
%28h%2B4%29%2A%28h-9%29h=180
-
%28h%5E2%2B4h-9h-36%29h=180
h%5E3-5h%5E2-36h-180=0

Using graphing software, taking a decimal approximation for the one real root, h=10.235; and then w and L can be evaluated.

Maybe the "difference" interpretation was the wrong one, and different results might happen if, L=9-h, but you can try that if you want, and solve to see what you get.