SOLUTION: We took a quiz in the form of a PSSA writing prompt, the question was: "A box with a square base and no lid is to be made from a square piece of metal by cutting 5cm squares from

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Question 359574: We took a quiz in the form of a PSSA writing prompt, the question was:
"A box with a square base and no lid is to be made from a square piece of metal by cutting 5cm squares from the corners and folding up the sides. If the volume of the box is 100cm cubed, find the dimensions of the square piece of metal. (Round to the nearest tenth.)
I received a poor grade because I used the wrong formula, and would like it if you could help me better understand how to get the correct answer? If not I will be attending school early to have a small conference with my teacher so that we may go over my quiz and evalute the appropriate answer.
I would appreciate your help very much, here is my "attempt.":
V=11cm^3V=LxWxh
h=5cm
100cm^3=LxWx5cm
L=x-10
W=x-10
100cm^3=(x-10)(x-10)5
100cm^3=(x^2-10x-10x+100)5
100cm^3=x^2-20x+100)5
100cm^3=x^2-20x+105
-100 -100
0=x^2-20x+5
(from here I could not factor so I went to the quadratic equation and got x=10 plus or minus sqrt (95) over 2)
I would appreciate your much needed help, Thank You for your time!
Found 2 solutions by vleith, mananth:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Up to hjere, you were golden
100=%28x%5E2-20x%2B100%295
Then you added 5. That 5 at the end is multiplying the other terms.
100=%28x%5E2-20x%2B100%295
20+=+%28x%5E2-20x%2B100%29
0+=+%28x%5E2-20x%2B80%29
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-20x%2B80+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-20%29%5E2-4%2A1%2A80=80.

Discriminant d=80 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--20%2B-sqrt%28+80+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-20%29%2Bsqrt%28+80+%29%29%2F2%5C1+=+14.4721359549996
x%5B2%5D+=+%28-%28-20%29-sqrt%28+80+%29%29%2F2%5C1+=+5.52786404500042

Quadratic expression 1x%5E2%2B-20x%2B80 can be factored:
1x%5E2%2B-20x%2B80+=+1%28x-14.4721359549996%29%2A%28x-5.52786404500042%29
Again, the answer is: 14.4721359549996, 5.52786404500042. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-20%2Ax%2B80+%29


So the two possible answers are 14.5 and 5.5
Since 5.5-10 would be negative, the only possible option is 14.5
14.5-10 = 4.5
Does 4.5 * 4.5 * 5 end up being close to 100?

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
"A box with a square base and no lid is to be made from a square piece of metal by cutting 5cm squares from the corners and folding up the sides. If the volume of the box is 100cm cubed, find the dimensions of the square piece of metal.
..
let sides of plate be x cm
5cm square is cut in the corners
..
the measure of the sides will reduce by 10 cm
sides of box = x-10
since it is folded at 5 cm the height will be 5 cm
..
the sides of the square box will be (x-10)
height = 5 cm
Volume V = 100
(x-10)(x-10)*5 = 100
(x^2-20x+100)*5 = 100
(x^2-20x+100) = 100/5
x^2-20x+100=20
x^2-20x+80=0
use quadratic formula
discriminant = 80
x=(20+sqrt(80))/2
=14.47 cm the length of the sheet metal
..
m.ananth@hotmail.ca