Triangle With Random Constraints?

Geometry Level 5

For a particular triangle, the reciprocal of the angles follows a harmonic progression, and two of the side lengths of this triangle are given as 4 and 5. Find the sum of all distinct possible values of the perimeter of this triangle.

\[31+\sqrt{21}\] \[2+\sqrt{13}+\sqrt{21}\] \[20+\sqrt{13}+\sqrt{21}\] \[29+\sqrt{13}+\sqrt{21}\] \[27\] \[63\] None of the other options No such triangle exists

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100 Day Summer Challenge

Triangle With Random Constraints?

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.