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computational of side lenght in quadrilateral

Source: LIMIT 2019 CAS2 P2

April 28, 2021
geometry

Problem Statement

Let ABCDABCD be a quadrilateral with sides ∣AB‾∣=2\left|\overline{AB}\right|=2, ∣BC‾∣=∣CD‾∣=4\left|\overline{BC}\right|=\left|\overline{CD}\right|=4 and ∣DA‾∣=5\left|\overline{DA}\right|=5. The opposite angles, ∠A\angle A and ∠C\angle C are equal. The length of diagonal BDBD equals <spanclass=′latex−bold′>(A)</span> 26<span class='latex-bold'>(A)</span>~2\sqrt6 <spanclass=′latex−bold′>(B)</span> 33<span class='latex-bold'>(B)</span>~3\sqrt3 <spanclass=′latex−bold′>(C)</span> 36<span class='latex-bold'>(C)</span>~3\sqrt6 <spanclass=′latex−bold′>(D)</span> 23<span class='latex-bold'>(D)</span>~2\sqrt3
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