You are building a rectangular kennel for your pet dog. You have purchased 300 F

Question

You are building a rectangular kennel for your pet dog. You have purchased 300 Ft of fencing and want to create a rectangular pen with dimensions that produce the largest area. Make an input-output table with width as the input and area as the output, using five inputs. Then draw a picture and find expressions for the width and length.

a) Input-output table

b) Picture of the pen (use x for the width)

c) Substitute the expressions for the length and width into the formula for area and multiply into a quadratic equation in standard form.

d) Find the vertex of this quadratic function. Interpret what the vertex is stating. What should the dimension of the pen be?

Explanation / Answer

a) Total Perimeter = P = 300

As we know perimeter for rectange = 2 (Length + Breadth ) : P = 2(L +W)

As W = width (x)

Length = P/2 - L = 150 - X

Area = (150-x)x = 150x - x2

Input (x)                            Output(150x-x2)

1) 10                                       1400

2) 20                                       2600

3) 30                                       3600

4)   50                                     5000

5) 100                                     5000

dA/dx = 150 -2x = 0

at x = 75 we get maximum area = 5625

Dimensioni of pen 75* 75 i.e. SQUARE

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