SOLUTION: Here is a story problem I do not have any idea how to firgure out can you help? You are building a poker table. You want it to be an octagon to seat 8 players. Each of the sides

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Question 203993This question is from textbook Mathematics For Technical trades
: Here is a story problem I do not have any idea how to firgure out can you help?
You are building a poker table. You want it to be an octagon to seat 8 players. Each of the sides is to be "x" inches long where the players will sit. If you cut the corners off at 45-degree angles to make the top,and the size of the wood is 54 x 54 inches, find the length of each side. Round the answer to the nearest 1/8 of an inch. Thanks Janet This question is from textbook Mathematics For Technical trades

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
x is the length of the hypotenuse of the isosceles right triangle that is cut from each corner of the 54" square

by Pythagoras, the length of a side of the triangle is [x / sqrt(2)]

the 54" length consists of one side of the octagon (x) plus two sides of the cut-out corner triangles (2[x / sqrt(2)])

x + 2[x / sqrt(2)] = 54 ___ x + x[sqrt(2)] = 54 ___ x = 54 / [1 + sqrt(2)]

x = 22.37 (approx) ___ or 22 3/8

good luck with the table