perplexus.info :: Shapes : Nine points in a square crossed triangle area puzzle

Nine points in a square crossed triangle area puzzle (Posted on 2023-02-13)

Nine points are given in a square having unit area.

Is it always possible to choose three of these points as the vertices of a triangle, such that the area of the triangle is at most 1/8?

Provide valid reasoning for your answer.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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solution via pigeon hole principle

| Comment 1 of 3

Divide the unit square into four squares each with side 1/2.

With nine points and four squares at least one square will contain three points.

Those three points determine a triangle which has maximum area when each leg is 1/2.

Area triangle <= (1/2)*bh = (1/2)*(1/2)*(1/2) = 1/8

Posted by xdog on 2023-02-13 19:40:07

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