Materials Needed: Graphing calculators Graph paper Scissors Rulers Tape Directions: 1.Cut out the box diagram. 2.Remove the shaded corners. 3.Fold along the fold lines. 4.Tape to secure the corners.

Meribelle Chocolates is famous for its mini chocolate truffles, which are packaged in foil covered boxes. The base of each box is created by cutting squares that are 4 cm on an edge from each corner of a rectangular piece of cardboard and folding the cardboard edges up to create a rectangular prism 4 cm deep. Meribelle Chocolates sells to a variety retailers and creates specific box sizes per requests; however, Meribelle Chocolates requires that their truffle boxes always be 4 cm deep and the bottom of each truffle box be a rectangle that is 2 ½ times as long as it is wide.

1.Meribelle Chocolates restricts box sizes to those which will hold plastic trays for a whole number of mini truffles. A box needs to be at least 2 cm wide to hold one row of mini truffles. Let L denote the length of a piece of cardboard from which a truffle box is made. What value of L corresponds to a finished box base for which the bottom is a rectangle that is 2 cm wide?

Answer For a finished box with width of 2 cm, the length must be 2.5(2) = 5 cm. Starting with a 2 cm by 5 cm box bottom, add 4 cm squares to each corner. The piece of cardboard should be = 10 cm wide and = 13 cm long. L = 13

2.Meribelle Chocolates has a maximum size box of mini truffles that it will produce for retail sale. For this box, the bottom of the truffle box base is a rectangle that is 50 centimeters long. What are the dimensions of the piece of cardboard from which this size truffle box base is made?

Answer If the bottom of the box is 50 cm long, then find the width, W, of the bottom with the equation 2.5W = 50. W = (0.4)(50) = 20 cm Add squares that are 4 cm 2 at each corner = 28 cm = 58cm

3.What is the area of the bottom of the box in terms of x ? 2.5 x x

3.What is the area of the bottom of the box in terms of L (length of the cardboard) ? L / 5 (L – 8)