Question #2b5bb

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Question #2b5bb

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Answer 1 · 2016-10-07T19:32:06

$x = 17$

Explanation:

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As $bar(AC)$ is the perpendicular bisector of $bar(BD)$ , we have $BC = CD$ .

As $AB$ and $AD$ are both hypotenuses of right triangles with legs of length $BC$ and $AC$ ( $triangle ACB$ and $triangle ACD$ , respectively), we know that $AB = AD$ . Equating the two, we get

$AB = AD$

$=> 2x-14 = 37-x$

$=> 3x = 51$

$=> x = 17$

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Question #2b5bb

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