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The shortest path between two points is a straight line. This is a mathematical fact, which can be proven in another question.

The diagonal of a quadrilateral is a straight line between two opposing (non-adjacent) vertices. The perimeter of a quadrilateral will include two separate paths between the same vertices. The difference is that these two paths are each composed of two linked line segments, so each of these paths will be longer than the diagonal.

Therefore, the length of the perimeter of a quadrilateral will be greater than twice the length of either diagonal.

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โˆ™ 2009-12-09 06:30:36
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Q: Prove that the perimeter of a quadrilateral is greater than the sum of the length of its diagonal?
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