2021 AMC 10B Problems/Problem 21
Revision as of 20:13, 11 February 2021 by Pi is 3.14 (talk | contribs) (→Video Solution by OmegaLearn (Logarithmic Tricks))
Contents
Problem
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 (Outlined)
double angle tangent to find angle ACE then trig
Solution (Quicksolve)
Assume that E is the midpoint of . Then,
and since
,
. By the Pythagorean Theorem,
. It easily follows that our desired perimeter is
~samrocksnature
Video Solution by OmegaLearn (Using Pythagoras Theorem and Similar Triangles)
~ pi_is_3.14