Math CentralQuandaries & Queries


A regular octagon is made up of 8 identical isosceles triangles. If the perimeter of each isosceles triangle and the hexagon are 58 cm and 168 com respectively, find the length of the identical sides of the triangle

Hi there.

The perimeter of one of the triangles is 58. That's two radii (r) and the length of one side (s):

58 = 2r + s

The perimeter of the octagon is 168. That's eight sides of length s:

168 = 8s.

Solve both equations for s, then eliminate s. Then solve for r.

Hope this helps,
Stephen La Rocque.

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