2001 AMC 10 Problems/Problem 24
Contents
Problem
In trapezoid ,
and
are perpendicular to
, with
,
, and
. What is
?
Solution
If and
, then
. By the Pythagorean theorem, we have
Solving the equation, we get
.
Solution 2
Simpler is just drawing the trapezoid and then using what is given to solve.
Draw a line perpendicular to AD that connects the longer side to the corner of the shorter side. Name the bottom part x and top part a.
By the Pythagorean theorem, it is obvious that (the RHS is the fact the two sides added together equals that). Then, we get
, cancel out and factor and we get
. Notice that
is what the question asks, so the answer is
Solution by IronicNinja
See Also
2001 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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All AMC 10 Problems and Solutions |
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