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 = whP=2(1 + w)

Answer:V = (5)(14 L - L^2) cm^3Step-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 to14 cm = W + L, which can be solved for either W or L.  Solving for W:  W = 14 cm - LThen the area of the rectangular base is A = W*L, or A = (14 cm - L)(L), orA = 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^2This is a quadratic equation.  Putting it into standard form yields:V = (5)(14 L - L^2) cm^3.  This is the desired quadratic formula.