Answer:
23cm by 24cm by 25 cm
Step-by-step explanation:
It was given that, the dimensions of a rectangle box are consecutive integers.
This means the dimension is of the form: [tex]x-1,x,x+1[/tex]
We know the volume of a box to be given as:
[tex]Volume=lbh[/tex]
This means that the volume in terms of x is :
[tex]Volume=x(x-1)(x+1)[/tex]
This volume is equal to 13800.
So we have the equation:
[tex]13800=x(x-1)(x+1)[/tex]
We expand to get:
[tex]13800=x^3-x[/tex]
[tex]x^3-x-13800=0[/tex]
We factor to obtain:
[tex](x-24)(x^2+24x+575)=0[/tex]
The only real solution is x=24.
Therefore the dimensions are: 24-1,24,24=1 OR 23,24,25
