The triangles ABD, ADC and ABC are similar (AA stands for "angle, angle" and means that the triangles have two of their angles equal).
If two triangles have two of their angles equal, the triangles are similar.
Therefore the sides of triangles are in proportion.

cross multiply

Use the Pythagorean theorem for calculate x:

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5 because 5×5= 25 and 5×5×5= 125
AC would be equivalent to 4. I know that the triangle is a 90, 45, 45 triangle which means 2 of the angles AND sides are equivalent to each other. Since angle B is 45 degrees angle C has to be 45 degrees. Same goes for the sides. Since AB=4, AC=4. It wouldn't be BC bc that's the hypotenuse or the longest part of the triangle. AC wouldn't be equal to 2 since it won't follow the rule of a 90, 45, 45 triangle. :|