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
the parallelogram has labels a, b, c, d, with intersection point e of the diagonals. the segment de is labeled $y + 2$, segment be is labeled $3y - 4$, segment ce is labeled $2y - 3$.

Explanation:

Step1: Use parallelogram diagonal property

In a parallelogram, diagonals bisect each other, so $y+2=2y-3$.

Step2: Solve for y

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

Step3: Calculate lengths of trail segments

Length of $AC = 2(y+2) = 2(5+2)=14$ miles
Length of $BD = 2(3y-4)=2(15-4)=22$ miles

Step4: Sum the two trail lengths

$\text{Total length} = 14 + 22$

Answer:

36 miles