Longer ClothesLines

Geometry Level 1

On the terrace of their house, Alice and Bob have three poles around which they've tied a rope in the following way:

The longer the rope, the more clothes they can hang. Who can hang more clothes?


Note: For simplicity, assume that the radii of the poles are all negligible.

Alice Bob It depends on the arrangement of the poles

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Agnishom Chattopadhyay by Agnishom Chattopadhyay , 22, India

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2 solutions

Siva Budaraju
Aug 10, 2017

Relevant wiki: Triangle Inequality

By the Triangle Inequality, 2 side lengths of a triangle added together have to be greater than the last. Alice's string takes up 2 sides of the triangle, and Bob's takes up the third, so Alice used more rope.

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Yep, Triangle Inequality is the way to go

Agnishom Chattopadhyay - 3 years, 10 months ago
William Huang
Aug 9, 2017

I think this problem can be done just with our eyes and our intuition. If we move Alice's (red) rope into a straight line and do the same with Bob's (blue) rope, it is a clear and obvious answer that the solution is Alice has a longer rope!

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