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19 February, 18:29

A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box?

V = lwh

P = 2 (l + w)

A. y = 5 (28 - x) (x)

B. y = 5 (28 - 2x) (x)

C. y = 5 (14 - x) (x)

D. y = 5 (14 - 2x) (x)

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Answers (1)
  1. 19 February, 21:52
    0
    Answer: C. y = 5 (14 - x) (x)

    Step-by-step explanation:

    The formula for determining the perimeter of a rectangle is expressed as

    Perimeter = 2 (L + W)

    If the rectangular base must have a perimeter of 28 cm, it means that

    28 = 2 (L + W)

    Dividing through by 2, it becomes

    14 = L + W

    L = 14 - W

    The formula for determining the volume of the rectangular box is expressed as

    Volume = LWH

    If H = 5 cm, then

    Volume,

    y = 5 (14 - W) (W)

    Looking at the options, W = x

    Therefore,

    y = 5 (14 - x) (x)
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