1957 AHSME Problems/Problem 31

Problem

A regular octagon is to be formed by cutting equal isosceles right triangles from the corners of a square. If the square has sides of one unit, the leg of each of the triangles has length:

$\textbf{(A)}\ \frac{2 + \sqrt{2}}{3} \qquad \textbf{(B)}\ \frac{2 - \sqrt{2}}{2}\qquad \textbf{(C)}\ \frac{1+\sqrt{2}}{2}\qquad\textbf{(D)}\ \frac{1+\sqrt{2}}{3}\qquad\textbf{(E)}\ \frac{2-\sqrt{2}}{3}$

Solution

$\boxed{\textbf{(B) }\frac{2-\sqrt{2}}2}$ .

1957 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 30	Followed by Problem 32
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1957 AHSME Problems/Problem 31

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