The parallelogram shown represents a map of the boundaries of a natural preserve. walking trails run from points a to c and from points b to d. the measurements shown represent miles.
what is the sum of the lengths of the two trails?
6 miles
12 miles
16 miles
36 miles

Walking trails AC and BD represent the diagonals of the parallelogram ABCD. As known the diagonals of the parallelogram bisects each other.

Then

Since DE=BE, then

y+2=3y-4,

2y=6,

y=3.

And BD = y+2+3y-4=3+2+9-4=10 miles.

Since y=3 miles and AE=CE, then

AC=2CE=2(2y-3)=2(6-3)=6 miles.

The  sum of the lengths of the two trails is

AC+Bd=10+6=16 miles.

correct choice is C

step-by-step explanation:

cats

m∠a is 90°

m∠b is 40°