# Difference between revisions of "2021 AMC 10B Problems/Problem 21"

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− | + | ==Problem== | |

+ | [url=https://aops.com/community/p20334805][size=150][b]Problem 21[/b][/size][/url] | ||

+ | A square piece of paper has side length <math>1</math> and vertices <math>A,B,C,</math> and <math>D</math> in that order. As shown in the figure, the paper is folded so that vertex <math>C</math> meets edge <math>\overline{AD}</math> at point <math>C'</math>, and edge <math>\overline{AB}</math> at point <math>E</math>. Suppose that <math>C'D = \frac{1}{3}</math>. What is the perimeter of triangle <math>\bigtriangleup AEC' ?</math> | ||

+ | |||

+ | <math>\textbf{(A)} ~2 \qquad\textbf{(B)} ~1+\frac{2}{3}\sqrt{3} \qquad\textbf{(C)} ~\sqrt{13}{6} \qquad\textbf{(D)} ~1 + \frac{3}{4}\sqrt{3} \qquad\textbf{(E)} ~\frac{7}{3}</math> | ||

+ | <asy> | ||

+ | pair A=(0,1); | ||

+ | pair CC=(0.666666666666,1); | ||

+ | pair D=(1,1); | ||

+ | pair F=(1,0.62); | ||

+ | pair C=(1,0); | ||

+ | pair B=(0,0); | ||

+ | pair G=(0,0.25); | ||

+ | pair H=(-0.13,0.41); | ||

+ | pair E=(0,0.5); | ||

+ | dot(A^^CC^^D^^C^^B^^E); | ||

+ | draw(E--A--D--F); | ||

+ | draw(G--B--C--F, dashed); | ||

+ | fill(E--CC--F--G--H--E--CC--cycle, gray); | ||

+ | draw(E--CC--F--G--H--E--CC); | ||

+ | label("A",A,NW); | ||

+ | label("B",B,SW); | ||

+ | label("C",C,SE); | ||

+ | label("D",D,NE); | ||

+ | label("E",E,NW); | ||

+ | label("C",CC,N); | ||

+ | </asy> | ||

+ | ==Solution== | ||

+ | A |

## Revision as of 19:28, 11 February 2021

## Problem

[url=https://aops.com/community/p20334805][size=150][b]Problem 21[/b][/size][/url] A square piece of paper has side length and vertices and in that order. As shown in the figure, the paper is folded so that vertex meets edge at point , and edge at point . Suppose that . What is the perimeter of triangle

## Solution

A