Question

The dimensions of a rectangle box are consecutive integers. If the box has a volume of 13800 cubic centimeters, what are it’s dimensions

Answer 1

23cm by 24cm by 25 cm

Explanation:

Answer 2

23cm by 24cm by 25 cm

Explanation:

It was given that, the dimensions of a rectangle box are consecutive integers.

This means the dimension is of the form:
`x-1,x,x+1`

We know the volume of a box to be given as:

`Volume=lbh`

This means that the volume in terms of x is :

`Volume=x(x-1)(x+1)`

This volume is equal to 13800.

So we have the equation:

`13800=x(x-1)(x+1)`

We expand to get:

`13800=x^3-x`

`x^3-x-13800=0`

We factor to obtain:

`(x-24)(x^2+24x+575)=0`

The only real solution is x=24.

Therefore the dimensions are: 24-1,24,24=1 OR 23,24,25