A word problem (geometry) with line segments

Question

The east side park has a large, triangular, dog walking path connecting points A, B, C. A human and dog drinking fountain is located half way on each side of the path, at the points D, E and F.

a) Given: AF = 7x- 60 and FC = 5x

AD = 4x + 10 and DB = 3x + 40

BE = 5x - 30 and EC = x + 90

Find the perimeter of the triangular path connecting points A, B and C, in feet.

Answer 1

Since the fountains are halfway,

AF = FC, solve for x and determine AC

AD = DB, same as above

BE = BE, same as above