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 = wh
P=2(1 + w)

Answer 1

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

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.

Answer 2

C

Explanation:

y = 5(14 – x)(x)