1990 AIME Problems/Problem 3
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Problem
Let be a regular
and
be a regular
such that each interior angle of
is
as large as each interior angle of
. What's the largest possible value of
?
Solution
The formula for the interior angle of a regular sided polygon is .
Thus, . Cross multiplying and simplifying, we get
. Cross multiply and combine like terms again to yield
. Solving for
, we get
.
and
, making the numerator of the fraction positive. To make the denominator positive,
; the largest possible value of
is
This is also achievable because the denominator is 1, making r a positive number.
See also
1990 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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