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an open box is made from a 40-cm by 80-cm piece of tin by cutting a square from each corner
and folding up the edges. The area of the resulting base is 2964 cm^2.
What is the length of the sides of the squares
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After cutting the squares from the corners and folding,
the dimensions of the base are (40-2x) cm and (80-2x) cm,
where x is the side of each square.
Now you write this quadratic equation for the base area
(40-2x)*(80-2x) = 2964 square centimeters.
Then you simplify it step by step
(20-x)*(40-x) = 741
800 - 40x - 20x + x^2 = 741
x^2 - 60x + 59 = 0
(x-59)*(x-1) = 0
and find the roots 59 and 1.
The root 59 is too big to be the side of the cut square,
so the only solution to the problem is 1 cm for the side of the squares.
CHECK. (40-2*1)*(80-2*1) = 2964 cm^2, the area of the base. ! correct !
Solved.
