Answer:
equation: x^2+12x-220 = 0
factored form: (x-10)(x+22) = 0
solution: x=10 or x=-22
dimensions: 4 cm, 11 cm, and 21 cm.
Explanation:
Given:
Volume = 924
dimensions of cuboid = 4, (x+1), (x+11)
Solution
Calculate volume
4(x+1)(x+11) = 924
simplify
(x+1)(x+11) = 231
Expand
x^2+12x+11 = 231
Simplify
x^2+12x-220 = 0
Factor
x^2-10x + 22x -220 = 0
x(x-10) + 22(x-10) = 0
(x-10)(x+22) = 0
x=10 or x=-22
Since x=-22 will give rise to negative dimensions, root will be rejected.
For x=10, the dimensions can be obtained by substituting x=10
x+1 = 11
x+11 = 21
So dimensions are
4 cm, 11 cm, and 21 cm.
Check: 4*11*21 = 924 checks.