an open box contains 80cm^3 and is made from a square piece of tinplate with 3cm squares cut from each of its 4 corners. Find the dimensions of the original piece of tinplate.

I see the equation

3(x-6)(x-6) = 80
3(x^2 - 12x + 36) = 80
3x^2 - 36x + 108 - 80 = 0
3x^2 - 36x + 28 = 0

Use the quadratice formula to find x

I got x=11.164

check 11.164-6 = 5.164

so the box is 5.164x5.164x3
which gives 80

Let the side of the square plate be x cm.

The height of the box is 3 cm.
The length & width are both (x-6) cm.
volume = length*width*height
=3*(x-6)*(x-6)
=80
x can then be obtained by solving
3(x-6)(x-6)=80

So why is the length and width x-6? where did the 6 come from can someone explain please?

Why did the tinplate go to the gym?

Because it wanted to get ripped! Okay, let's solve this puzzle.

Let's say the side length of the original square piece of tinplate is "x".

When we cut out the 3cm squares from each corner, the length of the box becomes (x - 2 * 3) = (x - 6) cm, and the height becomes (x - 2 * 3) cm as well.

The volume of the box is given as 80cm^3, so we can set up the equation:

Volume = length * width * height
80 = (x - 6) * (x - 6) * 3

Now we can solve for x:

80 = (x - 6)^2 * 3
80/3 = (x - 6)^2
26.67 = (x - 6)^2
√26.67 ≈ x - 6
x ≈ √26.67 + 6

So, the dimensions of the original piece of tinplate are approximately √26.67 + 6 cm by √26.67 + 6 cm.

Oh, and remember, don't confuse the tinplate for real weights at the gym. You might end up with some very confused muscles!

To find the dimensions of the original piece of tinplate, we need to work backwards.

Let's assume the original side length of the square tinplate is "x" cm.
When 3 cm squares are cut from each corner, the remaining shape will be a rectangular box with dimensions (x-2(3)) cm by (x-2(3)) cm by 3 cm.
The volume of the open box is given as 80 cm^3.

Therefore, we can write the equation as:
Volume of the box = Length x Width x Height
80 = (x - 2(3)) x (x - 2(3)) x 3

Simplifying, we have:
80 = (x - 6) x (x - 6) x 3
80 = (x - 6)^2 x 3
80/3 = (x - 6)^2
26.6667 = (x - 6)^2

Now, the next step is to find the square root of both sides to solve for "x - 6".

√(26.6667) ≈ 5.1649 = (x - 6)

Adding 6 to both sides, we get:
5.1649 + 6 ≈ 11.1649 = x

Therefore, the original side length of the square tinplate is approximately 11.1649 cm.