SOLUTION: An open box is to be made from a 10 cm by 20 cm rectangular piece of cardboard by cutting a square from each corner and folding up the sides. The area of the bottom of the box is

Question 118426: An open box is to be made from a 10 cm by 20 cm rectangular piece of cardboard by cutting a square from each corner and folding up the sides. The area of the bottom of the box is 96 cm squared. What is the length of the sides of the squares that are cut from the corners?
I really need help solving this algebraically. If you could help that would be amazing!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If you draw a picture, you can see that the dimensions of the bottom of the box are by

So the area of the bottom is

Now plug in the given area

Foil

Subtract 96 from both sides

Combine like terms

Rearrange the terms

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=4, b=-60, and c=104

Negate -60 to get 60

Square -60 to get 3600 (note: remember when you square -60, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 4 to get 8

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our possible solutions are:
or

However, since 13 is greater than 10, the solution is not possible since the square cutout cannot have a longer length than one of the sides.

So our only solution is

------------
Check:

Remember, the area is

Plug in the given area and

Multiply

Subtract

Multiply. Since the two sides of the equation are equal, this verifies our answer.
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