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Math Help - Find the dimensions of a square

  1. #1
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    Find the dimensions of a square

    A square walled city of unknown dimensions has four gates, one at the center of each side. A tree stands 20 m from the north gate. one must walk 14 m southward from the south gate and 1775m west before one can see the tree. what are the dimensions of the city?
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  2. #2
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    Quote Originally Posted by nikie1o2 View Post
    A square walled city of unknown dimensions has four gates, one at the center of each side. A tree stands 20 m from the north gate. one must walk 14 m southward from the south gate and 1775m west before one can see the tree. what are the dimensions of the city?
    1. Draw a sketch.

    2. You are dealing with similar right triangles. Use proportions:

    \dfrac{20}{\frac12 x} = \dfrac{34+x}{1775}

    Solve for x.

    Spoiler:
    You should come out with x = 250 m. The negative solution of the equation isn't very plausible here.
    Attached Thumbnails Attached Thumbnails Find the dimensions of a square-quad_stadt.png  
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    The sketch was very helpful. thank you !
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