EXPLANATION
We have an equilateral triangle because the 3 angles are congruent as shown in the picture and all legs are congruent:
So, 5x-12 = 3x - 4
Adding +12 to both sides:
5x - 12 + 12 = 3x - 4 + 12
Simplifying:
5x = 3x + 8
Subtracting both sides by -3x:
5x - 3x = 3x - 3x + 8
Simplifying:
2x = 8
Dividing both sides by 2:
x = 8/2
Simplifying:
x=4
Now, replacing in any equation, as 5x - 12:
5*(4) - 12= 8
In conclusion, all the legs are congruent and equal to 8.
Answer: DE= 8