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Honors Geometry

You work for a fencing company. A customer called, wanting to fence in his 1,320 square-foot rectangular garden. He ordered 148 feet of fencing, but you forgot to ask him for the width and length of the garden (these dimensions will determine some of the details of the order, so you need the information). You don't want the customer to think that you're incompetent, so you figure out the length and width from the information the customer has already given you. What are the dimensions? Hint, what is the area of the garden, and what is the perimeter of the garden? If you are having trouble using algebra to solve this problem, you may be able to get the answer through guess and check.

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  1. perimeter = 2 x + 2 y
    where x is width and y is length
    so 2 x + 2 y = 148
    x + y = 74
    also we know area = x*y = 1320
    so
    y = 1320/x
    so
    x + 1320/x = 74
    x^2 + 1320 = 74 x
    x^2 - 74 x = -1320
    add (74/2)^2 = 37^2 =1369 to both sides
    (x-37)^2 = 49
    x = 37 +/- 7
    x = 30 or x = 44
    well, I think this garden is 30 by 44 feet

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  2. Thanks :) It is 30 by 44 feet :)

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