SOLUTION: An open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. D

Question 1060643: An open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. Determine the dimensions of the squares that must be cut to create a box with a volume of 1008cm^3.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Dimensions x and y
Uniform sidelength of each square, w
Volume of box, v

w is also how high or tall the box.
Bottom area when flaps folded will be

MAIN STARTING EQUATION:

STEPS

-------Cubic equation in the unknown variable, w.

Make the substitutions and simplify from and the equation becomes .

You can try looking for zeros or roots based on Rational Roots theorem. The practical factorizations which would be useful for the term, would be ; so continue this by testing roots 1, 2, 3, 4, 6, 7, and see if any give remainder of 0 when using synthetic division.

(3 and 4.92 both will work).
Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!
.
An open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard
that has dimensions of 20 cm by 30 cm and folding up the sides. Determine the dimensions of the squares that must be cut
to create a box with a volume of 1008cm^3.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

(20-2x)*(30-2x)*x = 1008. = 1008, = 1008, = 252, = 0, One root is x= 3. So, one solution is x= 3. Two others are x= =~ 4.92 and x= =~ 17.08. The latest is TOOOOO big. Check. (20-2*3)*(30-2*3)*3 = 14*24*3 = 1008. Answer. One solution is x= 3. Another is x= =~ 4.92 Plot y =

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