Question

A cuboid with a volume of 924cm^3 has dimensions 4cm, (x+1)cm and (x+11). Show clearly that x^2+12x-220=0 solve the equation by factorisation, making sure you show the factorisation. Finally, find the dimensions of the cuboid,

Answer 1

`x^2+12x-220=0` -- Proved

`x = 10\ \ \ x = -22`

Explanation:

Given

`Volume = 924cm^3`

`Dimension: 4cm; (x+1)cm; (x+11)cm`

Required

Show that
`x^2+12x-220=0`

The volume is calculated as:

`4 * (x + 1) * (x + 11) = 924`

Open the brackets

`(4x + 4) * (x + 11) = 924`

`4x^2 + 44x + 4x + 44 = 924`

`4x^2 + 48x+ 44 = 924`

Collect Like Terms

`4x^2 + 48x+ 44 - 924=0`

`4x^2 + 48x -880=0`

Divide through by 4

`(4x^2)/(4) + (48x)/(4) -(880)/(4)=0`

`x^2+12x-220=0`

Solving further:

Expand the expression

`x^2 + 22x - 10x - 220 = 0`

Factorize:

`x(x + 22) - 10(x + 22) = 0`

`(x - 10)(x + 22) = 0`

Split:

`x - 10 = 0;\ \ \ x + 22 = 0`

`x = 10\ \ \ x = -22`