Suppose that you need to fence a rectangular play area in your backyard for your child or pet. Further, suppose that you know the length must be 8 feet longer than the width. The back of your house will serve as one side of the fenced area. **Note:** The perimeter (distance around) of a general rectangle is *P* = 2*L* + 2*W*, and its area is *A* = *L* x *W*. In this situation, *P* = *L* + 2*W*.

- (Write the value of area chosen.)

If your last name begins with the letter | Choose an area that must be fenced in this range (in square feet) |

A–E | 3,000–3,999 |

F–I | 4,000–4,999 |

J–L | 5,000–5,999 |

M–O | 6,000–6,999 |

P–R | 7,000–7,999 |

S–T | 8,000–8,999 |

U–Z | 9,000–9,999 |

- (Write the equation of the perimeter in terms of the length,
*L*, only.) - (Write the area equation in terms of the length,
*L*, only.) - (What can you observe about the characteristics of that quadratic area function? Will this quadratic function’s graph cross the horizontal axis? How do you know?)
- (Show all your work for finding both the length and the width of this rectangular fenced area.)
- (Show all your work for calculating the cost of the fence.)
- (Show all your work for calculating the cost per square foot of the fenced area.)
- (What observations and conclusions can you make about the results of them?)
- (List the intelli
**path**Learning Nodes that were helpful with this assignment,)