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 = wh

P=2 (1 + w)

V = (5) (14 L - L^2) cm^3

Step-by-step explanation:

Let the dimensions of the rectangular base be W by L and the height be H.

The perimeter must be 28 cm, so 28 cm = 2 (W) + 2 (L). This reduces to

14 cm = W + L, which can be solved for either W or L. Solving for W:

W = 14 cm - L

Then the area of the rectangular base is A = W*L, or A = (14 cm - L) (L), or

A = 14L - L^2.

The volume of the box is then V = A*H.

Because H = 5 cm, the volume is V = (5 cm) A, or

V = (5 cm) (14L - L^2) cm^2

This is a quadratic equation. Putting it into standard form yields:

V = (5) (14 L - L^2) cm^3. This is the desired quadratic formula.