Problema Solution
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 96 ft ^2. What is the length of the sides of the squares that are cut from the corners?
Answer provided by our tutors
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