1994 AIME Problems/Problem 10
Problem
In triangle angle
is a right angle and the altitude from
meets
at
The lengths of the sides of
are integers,
and
, where
and
are relatively prime positive integers. Find
Solution
Since , we have
. It follows that
and
, so
and
are in the form
and
, respectively.
By the Pythagorean Theorem, we find that , so
. Letting
, we obtain after dividing through by
,
. As
, the pairs of factors of
are
; clearly
, so
. Then,
.
Thus, , and
.
See also
1994 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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All AIME Problems and Solutions |