2023 AMC 10B Problems/Problem 24
Revision as of 14:20, 15 November 2023 by Technodoggo (talk | contribs)
Solution 1
Notice that this we are given a parametric form of the region, and is used in both
and
. We first fix
and
to
, and graph
from
:
Now, when we vary from
to
, this line is translated to the right
units:
We know that any points in the region between the line (or rather segment) and its translation satisfy and
, so we shade in the region:
We can also shift this quadrilateral one unit up, because of . Thus, this is our figure:
The length of the boundary is simply (
can be obtained by Pythagorean theorem, since we have side lengths
and
.). This equals
~Technodoggo