A Geometry test

Geometry Level 2

Given a triangle ABC satisfying BC=1 and AC=5. If the length of AB is an integer, then what is the length of AB?


The answer is 5.

Tin Le by Tin Le , 15, Vietnam

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2 solutions

Chris Lewis
May 13, 2019

By the triangle inequality, we need

A B < A C + B C = 6 AB<AC+BC=6

and A B > A C − B C = 4 AB>AC-BC=4

The only integer solution is A B = 5 AB=\boxed5

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Cos(C)<1. This implies length of AB must be greater than 4. But this length must be less than 5+1 or 6. Therefore length of AB is 5

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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