Question

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)

Answer 1

Answer: C

Explanation:

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Answer 2

Answer: C. y = 5(14 – x)(x)

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)