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: 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)