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If someone is attached to a 20 ft rope, which is attached to the corner of a building, how far can they move? If the bulding is 22 ft X 15 ft?

  • Math -

    The way you worded the question, the answer is 20 ft

    I have seen this question worded in the following way:
    A dog with a 20 ft leash is tied to the corner of a building which is 22 ft by 15ft.
    What is the area that the dog can cover?
    make a sketch.
    clearly he can reach 20 ft down along the building.
    If he goes the other way, he can move around the corner, cover the 15 ft along the width of the building and wrap around another 5 ft down the length of the opposite side of the long building
    So I see 3/4 of a circle with radius 20, and 1/4 of a circle with radius 5

    total area = (3/4)π(20)^2 + (1/4)π(5^2)
    = 300π + (25/4)π = (1225/4)π or 306.25π or appr 962 ft^2

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