Answer:
4cm, 11cm, and 21cm
Step-by-step explanation:
The given dimensions of the cuboid are:
4cm , (x+1)cm,( x+11)cm
The volume of the cuboid is given as 904cm³
We know volume of a cuboid is given as:
V=LBH
We substitute the dimensions to get:
[tex]4(x + 1)(x + 11) = 924[/tex]
Divide through by 4.
[tex](x + 1)(x + 11) = 231[/tex]
We expand on the left to get:
[tex] {x}^{2} + 11x + x + 11 = 231[/tex]
[tex] {x}^{2} + 12x + 11 - 231= 0[/tex]
This simplifies to:
[tex] {x}^{2} + 12x - 220= 0[/tex]
To factor this expression we obtain:
[tex] {x}^{2} + 22x - 10x - 220 = 0[/tex]
[tex] {x}(x + 22) - 10(x + 22) = 0[/tex]
[tex](x + 22)(x - 10) = 0[/tex]
[tex]x = 10 \: or \: - 22[/tex]
But the dimension must be positive:
hence x=10
Therefore the dimensions are 4cm, 11cm, and 21cm
