2021 Fall AMC 10B Problems/Problem 15
Problem
In square , points
and
lie on
and
, respectively. Segments
and
intersect at right angles at
, with
and
. What is the area of the square?
Solution
Note that Then, it follows that
Thus,
Define
to be the length of side
then
Because
is the altitude of the triangle, we can use the property that
Substituting the given lengths, we have
Solving, gives
and
We eliminate the possibilty of
because
Thus, the side lengnth of the square, by Pythagorean Theorem, is
Thus, the area of the sqaure is
Thus, the answer is
~NH14
See Also
2021 Fall AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.