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.
