Halving a Triangular Lawn

★ 7/10plane geometry trigonometry Law of Cosines AM-GM inequality Triangle Geometry

Problem

A triangular lawn $\triangle ABC$ has side lengths $30$ , $40$ , and $50$ meters. Points $D, E$ lie on the sides of the triangle, and the segment $DE$ divides the lawn into two parts of equal area. If a water pipe is laid along $DE$ , find the minimum possible length of the pipe, in meters.

Answer

Solution

Difficulty	7/10
Topics	plane geometry, trigonometry, Law of Cosines, AM-GM, inequality, Triangle Geometry

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