Question

Question #2b5bb

Answer 1

`x = 17`

Explanation:

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`