Question

A cuboid with a volume of 924 cm^3 has dimensions

4 cm, (x + 1) cm and (x + 11) cm.
Find the longest length of the Cuboid.

Answer 1

21

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