# Question #39008

##### 2 Answers

#### Answer:

The dimensions of the box are

#### Explanation:

It always helps to draw a diagram.

Originally, the box had dimensions

If we were to fold the red areas up to form the sides of the box, the box would have height

But the problem says the volume is

Now we have this system:

Solving for

Plugging this in for

We know that

Note that these are the dimensions on the original metal sheet. When we take out the

When you check the dimensions of

Now let the length of the box be **a** cm and its width be **b** cm.

Then

To keep the volume and height of the box at given value its **base area** **must be fixed** at

To construct the box 4 squares of dimension

So

Now let us see what happens if we try to find out **a** and **b** using equation (1) and (2).

Combining (1) and (2) we get

Now trying to find out

**This shows that real solution is not possible with sheet area 1200cm^2.**

But a real solution is possible with a minimum value of the perimeter of the base of the box i.e.

for real values of **a** and **b**,

This gives

and

Then by relation (2)

Now with this sheet area of

And the the **dimension of the box** then will be