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Rest in peace, Bahman - Iran First Round 2018, P13

Source:

March 7, 2021
geometric optimization

Problem Statement

Bahman wants to build an area next to his garden's wall for keeping his poultry. He has three fences each of length 1010 meters. Using the garden's wall, which is straight and long, as well as the three pieces of fence, what is the largest area Bahman can enclose in meters squared?
<spanclass=′latex−bold′>(A)</span> 100<spanclass=′latex−bold′>(B)</span> 50+253<spanclass=′latex−bold′>(C)</span> 50+502<spanclass=′latex−bold′>(D)</span> 753<spanclass=′latex−bold′>(E)</span> 300<span class='latex-bold'>(A)</span>\ 100 \qquad<span class='latex-bold'>(B)</span>\ 50+25 \sqrt 3\qquad<span class='latex-bold'>(C)</span>\ 50 + 50\sqrt 2\qquad<span class='latex-bold'>(D)</span>\ 75 \sqrt 3 \qquad<span class='latex-bold'>(E)</span>\ 300
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