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,

Answer 1

Answer:

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.