Question #2b5bb

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Question #2b5bb

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Answer 1 · 2016-10-07T19:32:06

$x = 17$ $x = 17$

Explanation:

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As $¯ ¯¯¯¯ ¯ A C$ $bar(AC)$ is the perpendicular bisector of $¯ ¯¯¯¯ ¯ B D$ $bar(BD)$ , we have $B C = C D$ $BC = CD$ .

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

$A B = A D$ $AB = AD$

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

$\Rightarrow 3 x = 51$ $=> 3x = 51$

$\Rightarrow x = 17$ $=> x = 17$

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Question #2b5bb

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