Farhan's problem of Sides

Geometry Level 2

The largest side of a triangle is twice the smallest and the largest angle is thrice the smallest. If its area is 32√3, find the length of the largest side.


The answer is 16.

Farhanur Rahman by Farhanur Rahman , 19, Bangladesh

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2 solutions

This description only applies to a right triangle with angles 30-90-60 and sides 16-8-8root3

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Farhanur Rahman
Feb 4, 2018

Thee angles are 30°, 60° and 90°. The sides of the triangle are a,√3a,2a. The triangle is right because 2²=1²+√3². Area=½x√3axa=32√3 Which yields a=8 giving the largest side 16. So the answer is 16.

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