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.

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.

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Bơ 4 years 2021-08-08T11:10:17+00:00 1 Answers 682 views 0

Answers ( )

  1. Delwyn
    0
    2021-08-08T11:11:40+00:00
    Reply

    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

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