SOLUTION: The volume of a right rectangular solid with a square base is 108in^3. Find the dimensions of the box if the height of the box is the same as the primeter of the box.

Algebra ->  Volume -> SOLUTION: The volume of a right rectangular solid with a square base is 108in^3. Find the dimensions of the box if the height of the box is the same as the primeter of the box.       Log On


   

Question 769328: The volume of a right rectangular solid with a square base is 108in^3. Find the dimensions of the box if the height of the box is the same as the primeter of the box.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
As written, the problem is unclear. Perimeter is applied to 2-dimensional figures. Perimeter is the distance all around a 2-dimensional figure. The word perimeter can not be applied to the 3-dimansional box. It could be applied to the square base of the box or to the rectangular side of the box.

x= length of a side of the square base of the box
h= height of the box
4x= perimeter of the base of the box
2x%2B2h= perimeter of the side of the box
x%5E2= area of the base of the box
%28x%5E2%29h= volume of the box

The height of the box being the same as the perimeter of the side of the box,
h=2x%2B2h,
does not make sense, because x and h must be both positive inch measurements.

It must be that the height of the box is the same as the perimeter of the base of the box,
h=4x
Then the volume of the box is
%28x%5E2%29%284x%29=108in%5E2
Solving:
%28x%5E2%29%284x%29=108in%5E2-->4x%5E3=108in%5E2-->x%5E3=108in%5E2%2F4-->x%5E3=27in%5E2-->highlight%28x=3in%29
Then, the height of the box, h=4x, is
h=4%283in%29-->highlight%28h=12in%29