Question

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

Answer 1

The answer is

C.16

I checked myself

Explanation:

on edge

Answer 2

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

Then

• DE=BE;
• AE=CE.

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.

Answer: correct choice is C