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Question 24

In quadrilateral $$ABCD$$, $$AB=10$$, $$BC=33$$, $$CD=10$$ and $$DA=15$$. If $$BD$$ is an integer then $$BD$$ is


Correct Answer: 24

Solution

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In triangle $$ABD$$, the triangle inequalities give $$5<BD<25$$. In triangle $$BCD$$, they give $$23<BD<43$$. Therefore the only integer satisfying both sets of inequalities is $$BD=24$$.

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