geometry

A square measures 18feet 6inches in length. If an octagon is inscribed in the square, then how long should each side of the octagon be?

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asked by Cathy
  1. Look at one of the corner triangles.
    Let each side of the octogon be x
    so the hypotenuse of that triangle is x
    let the other two sides be y each
    y^2 + y^2 = x^2
    2y^2 = x^2
    √2 y = x
    y = x/√2

    then x/√2 + x + x/√2 = 18.5
    multiply each term by √2
    x + √2 x + x = 18.5√2
    x(1 + √2 + 1) = 18.5√2
    x = 18.5√2/(2+√2) or appr. 7.66 ft or 7 feet 8 inches

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    posted by Reiny
  2. thank you very much

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    posted by Cathy

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