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max area of quadrilateral with sides 20,20,14,13 and right ange between 20s

Source: 2016 (-17) Swedish Mathematical Competition p1

August 31, 2020
geometryareaareasmax

Problem Statement

In a garden there is an LL-shaped fence, see figure. You also have at your disposal two finished straight fence sections that are 1313 m and 1414 m long respectively. From point AA you want to delimit a part of the garden with an area of at least 200200 m2^2 . Is it possible to do this? https://1.bp.blogspot.com/-VLWIImY7HBA/X0yZq5BrkTI/AAAAAAAAMbg/8CyP6DzfZTE5iX01Qab3HVrTmaUQ7PvcwCK4BGAYYCw/s400/sweden%2B16p1.png