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

Explanation:

Step1: Diagonals bisect in parallelogram

AE = EC, BE = ED

Step2: Solve for y using AE=EC

$y + 2 = 2y - 3 \implies y = 5$

Step3: Calculate AC length

AE = $5 + 2 = 7$, AC = $7 + 7 = 14$

Step4: Calculate BD length

BE = $3(5) - 4 = 11$, BD = $11 + 11 = 22$

Step5: Sum of trails

AC + BD = $14 + 22 = 36$

Answer:

D. 36 miles