open-top box problem, have been working on it for a while and cannot figure it out!!?

Question

I have a 14in by 11 in cardboard box. I need to cut 'x' (a tiny square) off each of the four corners so it can be folded into a box. the botton of it has an area of 80in^2. what size square should be cut from each corner?

Answer 1

Let X be the side of each of the squares. Figure the new width and length and set it to 80... solve for X.

You cut the length of one square (X) from each side, so the length of the base will be 14 - 2X.
Similarly, you cut the width of one square (X) from each side, so the width of the base will be 11 - 2X

So the bottom will be L * W.

(14 - 2X)(11 - 2X) = 80

Now solve for X, by multiplying through:
154 - 22X -28X + 4X^2 = 80

Group everything to get:
4X^2 - 50X + 154 - 80 = 0

4X^2 - 50X + 74 = 0

Divide everything by 2:
2X^2 - 25X + 37 = 0

Using the quadratic equation, you can solve for X.
One value will make for a negative area. Thus the only answer is X = 1.7154 in.

Answer 2

The bottom of the box will have area (14 - 2x)(11 - 2x). It's a quadratic equation once you expand this product. Set it equal to 80 and solve. This is the simplest solution i think. Hope this helps. Good luck

Answer 3

The bottom of the box will have area (14 - 2x)(11 - 2x). It's a quadratic equation once you expand this product. Set it equal to 80 and solve.