a) Since the triangles are congruent, and ΔABC is congruent to ΔDEF, segments AB and DE have the same value. Therefore, you can use algebra to solve for x when using the knowledge that (12 - 4x) is equal to (15 - 3x).
To solve:
12 - 4x = 15 - 3x
12 = 15 + x
-3 = x
Therefore, x is equal to -3.
b) To find the value of AB, plug in the value of x found in part a).
12 - 4x
12 - 4(-3)
12 - (-12)
12 + 12 = 24
Thus, segment AB is equal to 24.
c) As shown in part b), plug in the value of x found in part a) to find the value of segment DE.
15 - 3x
15 - 3(-3)
15 - (-9)
15 + 9 = 24
Thus, segment DE is also equal to 24.
We can confirm the knowledge of the equal side lengths because the triangle are congruent. This means that all the side lengths in the triangle are the same, which is confirmed when algebraically plugging in the value of x to solve for the values of the segments AB and DE.
I hope this helps!