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: Use the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So \(y + 2=2y - 3\).

Step2: Solve for \(y\)

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Step3: Find the length of one part of a diagonal

Substitute \(y = 5\) into \(y + 2\), we get \(5+2=7\). Substitute \(y = 5\) into \(3y-4\), we get \(3\times5-4=15 - 4=11\).

Step4: Calculate the sum of the lengths of the two diagonals

The sum of the lengths of the two diagonals \(AC\) and \(BD\): \((7 + 7)+(11+11)=14 + 22=36\) (Since diagonals bisect each other, total length of a diagonal is twice the length of its half - part)

Answer:

36 miles