Final answer:
To find x and BC, set the corresponding sides of the triangles equal to each other and solve for x. Then substitute the value of x to find BC.
Step-by-step explanation:
To find x and BC, we need to set the corresponding sides of the triangles equal to each other. From the given information, we have AC = 2x + 7, DF = 5x - 5, and EF = 5x. Since AABC = ADEF, we can set AC = DF and solve for x:
2x + 7 = 5x - 5
3x = 12
x = 4
Now that we have x, we can find BC by substituting the value of x back into the expression for AC:
AC = 2x + 7
AC = 2(4) + 7 = 15
Therefore, x = 4 and BC = 15.