# 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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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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