Question 328356: Box Construction. An open box is to be made from a 10-ft by 20-ft rectangular piece of cardboard by cutting a square from each corner. The area of the bottom of the box is to be 96ft^2. What is the length of the sides of the squares that are cut from the corners?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! An open box is to be made from a 10-ft by 20-ft rectangular piece of cardboard by cutting a square from each corner.
The area of the bottom of the box is to be 96ft^2.
What is the length of the sides of the squares that are cut from the corners?
:
let x = length of the sides of the removed squares
:
Then the dimensions of the box will be: (10-2x) by (20-2x) by x
:
The area of the bottom is given as 96 sq/ft
therefore:
(10-2x)*(20-2x) = 96
FOIL
200 - 20x - 40x + 4x^2 = 96
Arrange as a quadratic equation
4x^2 - 60x + 200 - 96 = 0
4x^2 - 60x + 104 = 0
Simplify, divide by 4
x^2 - 15x + 26 = 0
Factors to
(x-13)(x-2) = 0
Two solutions
x = 13 ft, does not make sense
and
x = 2 ft, is the length of the side of the removed squares
:
:
Check solution by finding the area:
[10 - 2(2)] * [20 - 2(2)] =
6 * 16 = 96
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