2023 AMC 12B Problems/Problem 17
Solution
The length of the side opposite to the angle with is longest.
We denote its value as
.
Because three side lengths form an arithmetic sequence, the middle-valued side length is .
Following from the law of cosines, we have
By solving this equation, we get .
Thus,
.
Therefore, the area of the triangle is
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
See Also
2023 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 16 |
Followed by Problem 18 |
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All AMC 12 Problems and Solutions |
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