Answer:
[tex]10cm\times 11 cm\times 12 cm[/tex]
Step-by-step explanation:
We are given that
Volume of water=1320 ml=1320 cubic cm
1ml=1 cubic cm
One dimension of rectangular prism=l=10 cm
Length,width and height are consecutive whole number
Breadth of rectangular prism=x+1
Height of rectangular prism=x+2
Volume of rectangular prism=lbh
Using the formula
[tex]1320=10(x+1)(x+2)[/tex]
[tex]x^2+x+2x+2=\frac{1320}{10}=132[/tex]
[tex]x^2+3x+2-132=0[/tex]
[tex]x^2+3x-130=0[/tex]
[tex]x^2+13x-10x-130=0[/tex]
[tex]x(x+13)-10(x+13)=0[/tex]
[tex](x-10)(x+13)=0[/tex]
[tex]x-10=0\implies x=10[/tex]
[tex]x+13=0\implies x=-13[/tex]
x=-13
It is not possible because length cannot be negative.
Length of rectangular prism=10 cm
Breadth of rectangular prism==10+1=11 cm
Height of rectangular prism==10+2=12 cm
Dimensions of the prism is given by
[tex]10cm\times 11 cm\times 12 cm[/tex]
