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math hw (algebra)

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On the sidewalk the distance from the dormitory to the cafeteria is 400 meters. By cutting across the lawn, the walking distance is shortened to 300 meters. how long is each part of the L shaped sidewalk?

  • math hw (algebra) - ,

    I visualize a right angled triangle with sides
    y, 400-y, and hypotenuse 300

    There will be large numbers , so here is a little trick
    let x be multiples of 100
    so we have
    x, 4-x, and 3 as the sides of a right-angled triangle

    x^2 + (4-x)^2 = 3^2
    x^2 + 16 - 8x + x^2 = 9
    2x^2 - 8x + 7 = 0
    x = (8 ± √8)/4
    = 2.7071 or 1.2929
    but x was a multiple of 100

    so one leg was 270.71 , the other 400-270.71 or 129.29 m

    or

    one leg was 129.29 , then the other leg was 270.71

    check
    270.71^2 + 129.29^2 = 89999.8 or appr 90000 = 300^2

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