Answer:
21
Step-by-step explanation:
Volume of a cuboid is given by
V = l*w*h
924 = 4 (x+1) (x+11)
FOIL
924 = 4(x^2 +11x+x+11)
924 = 4(x^2+12x+11)
Divide each side by 4
231 = (x^2+12x+11)
Subtract 231 from each side
0 = x^2 +12x +11-231
0 = x^2 +12x - 220
Factor
0 = (x+22) (x-10)
Using the zero product property
x+22 =0 x-10 =0
x=-22 x=10
We cannot have a negative length
x=10
The side lengths are 4, 10+1, 10+11
4,11,21
The longest is 21
