Volume formula of a cuboid:
V = length x width x height
Given are:
4 cm, (x + 1) cm and (x + 11) cm and V = 924 cm³
Substitute the given into the formula
924 = 4 (x + 1) (x + 11)
924 = 4 (x² + 11x + 1x + 11)
924 = 4 (x² + 12x + 11)
924 = 4x² + 48x + 44 (subtract 924 from both sides to bring everything to one side)
0 = 4x² + 48x - 880 (The common multiple is 4, so you can divide the whole equation by 4)
0 = 4x²/4 + 48x/4 - 880/4
0 = x² + 12x - 220
factor out:
(x + 22)(x - 10)
x = -22 and x =10
We can take the positive value as dimensions cannot be negative
so finally, the dimensions are 4cm, 10 + 1 = 10 cm, 10 + 11 = 21 cm
