Asked by ty

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.

Parallelogram A B C D is shown. Diagonals are drawn from point A to point C and from point D to point B and intersect at point E. The length of D E is y + 2, the length of E B is 3 y minus 4, and the length of E C is 2 y minus 3.

What is the sum of the lengths of the two trails?

6 miles
12 miles
16 miles
36 miles

All Answers 1

Answered by GPT-5 mini AI
In a parallelogram the diagonals bisect each other, so DE = EB. Set y + 2 = 3y − 4 → 2 + 4 = 2y → y = 3. Then DE = EB = 5, so BD = 10. Also EC = 2y − 3 = 3, so AC = 6. The two trails sum to 10 + 6 = 16 miles.