Final answer:
After setting up an equation based on the congruency of triangles ABC and DEF, we solve for x and find that x = 7. We substitute x back into the expression for DE to find that the length of DE is 41, which is not an option provided by the student.
Step-by-step explanation:
The question involves solving for a variable given the congruency of two triangles and algebraic expressions for their corresponding sides. We know that if triangles ABC and DEF are congruent, then their corresponding sides are equal in length. Therefore, we can set up an equation where AB (5x + 6) is equal to DE (7x - 8). The equation is:
5x + 6 = 7x - 8
To find the value of x, we'll subtract 5x from both sides of the equation:
6 = 2x - 8
And then add 8 to both sides:
14 = 2x
Dividing both sides by 2 yields:
x = 7
Once we have the value of x, we can substitute it back into the expression for DE to find its length:
DE = 7x - 8
DE = 7(7) - 8
DE = 49 - 8
DE = 41
Therefore, the correct option is not listed in the choices provided by the student. The value of x is 7, and the length of DE is 41.