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)
y = 5(28 – x)(x)
y = 5(28 – 2x)(x)
y = 5(14 – x)(x)
y = 5(14 – 2x)(x)

Answer 1

Perimeter: 2(l + w) = 28 ⇒ l + w = 14. Let x = one side, so the other side = 14 − x. Height = 5, so

V = 5 · x · (14 − x) = 5(14 − x)(x).

(Equivalently V = −5x^2 + 70x.)