Answer: D. 82 units
==========================================================
Explanation:
Sides BD and GE are the same length because they are opposite the angles marked with one tickmark. Whatever this angle measure is, it's the same for angles C and F. This leads to the congruent sides.
Solve for x
BD = GE
4x-9 = 2x+15
4x-2x = 15+9
2x = 24
x = 24/2
x = 12
Use that x value compute the length of side BD
BD = 4x-9 = 4*12-9 = 48-9 = 39
You should find that GE is also 39 when plugging in x = 12, which helps confirm the correct x value.
Once we know all three sides of triangle BCD, we can find its perimeter
BC+CD+BD = 17+26+39 = 82
That's the perimeter of triangle BCD, but the two triangles are mirror copies of each other. So they have the same perimeter (because they have the same corresponding side lengths).
