Track / Stage 4 / 261 of 340 #521 of 1964

Problem 521

AMC 12 late, AIME early

Geometry Difficulty 4.9 Multiple choice

18.73 A regular octagon is formed by cutting off equal isosceles right triangles from the corners of a square. If the side length of the square is 1, then the length of the legs of these triangles is

Pick one

Official solution

[Solution] Let the length of one leg of the cut-off isosceles right triangle be $x$ , then the length of the base is $\sqrt{2} x$ .
Then
$x+\sqrt{2} x+x=1 .$

We get
$x=\frac{2-\sqrt{2}}{2} \text {. }$

Therefore, the answer is $(B)$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.