SOLUTION: A box with an open top has a square base and four sides of equal height. The volume of the box is 200 ft cubed. The height is three feet greater than both the length and width. If

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Question 780186: A box with an open top has a square base and four sides of equal height. The volume of the box is 200 ft cubed. The height is three feet greater than both the length and width. If the surface area is 185 ft squared, what are the dimensions of the box?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A box with an open top has a square base and four sides of equal height.
The volume of the box is 200 ft cubed. The height is three feet greater than both the length and width.
If the surface area is 185 ft squared, what are the dimensions of the box?
:
Let s = the length of the sides of the square bottom
then
(s+3) = the height
:
Surface area:
4(s(s+3)) + s^2 = 185
4s^2 + 12s + s^2 - 185 = 0
A quadratic equation
5s^2 + 12s - 183 = 0
You can use the quadratic formula to find s, but this will factor to
(5s+37)(s-5) = 0
The positive solution is all we want here
s = 5 ft is the length of the square sides
then
5 + 3 = 8 ft is the height
:
Check by finding the volume
V = 5 * 5 * 8
V = 200 cu/ft