what is the length of the sides of the squares?

Question

An open box is made from a 10-cm by 20-cm piece of tin by cutting a square from each corner and folding up the edges. the area of the resulting base is 96cm^2. what is the length of the sides fo the squares?

Answer 1

<------------ 10 ------------>
^.......| .................... |
| ...... x ................... x
|-- x --|-----------------|-- x ---
| ...... | ... 10 - 2x ... |
| ...... | .................... |
20... | 20 - 2x ....... |
| ...... | .................... |
| ...... | .................... |
|-- x --|-----------------|-- x ---
| ...... x ................... x
v.......| .................... |

From the width you are cutting off 2x, from the length another 2x. So the area of the base is:

(10-2x)(20-2x) which equals 96.

Now you can expand this out into an equation and solve for x:
(200-60x+4x²) = 96

4x² - 60x + 200 - 96 = 0
4x² - 60x + 104 = 0
x² - 15x + 26 = 0
(x - 2)(x - 13) = 0

So x is either 2 or 13, but only one of these makes sense... can you tell which?

Obviously you can cut more than half the shortest dimension so the only reasonable answer is each square cutout is 2 cm on a side.

Answer 2

10 x 20
cut out 1 cm square we get 8 x 18 = 144
cut out 2 cm square we get 6 x 16 = 96

the square is 2cm long

Answer 3

4cmx4cm squares were cut out, resultant leftover (that was folder was 6cm x 16cm (=96cm2 area)