SOLUTION: The bottom and top of a box are rectangles twice as long as they are wide. Find the volume of the box if it is 4 ft high and has a total surface area of 220 ft�.

Question 198086: The bottom and top of a box are rectangles twice as long as they are wide. Find the volume of the box if it is 4 ft high and has a total surface area of 220 ft�.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The bottom and top of a box are rectangles twice as long as they are wide.
Find the volume of the box if it is 4 ft high and has a total surface area of 220 ft�
:
Let x = the width
then
2x = the length
:
The box dimensions: 2x by x by 4
Given the surface area:
2(2x*x) + 2(2x*4) + 2(x*4) = 220
:
4x^2 + 16x + 8x = 220
A quadratic equation:
4x^2 + 24x - 220 = 0
simplify, divide by 4
x^2 + 6x - 55 = 0
Factor
(x+11)(x-5) = 0
The positive solution is what we want here:
x = 5 ft is the width
then
2(5) = 10 ft is the length
:
Find the volume
10 * 5 * 4 = 200 cu/ft is the volume
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