the parallelogram shown represents a map of the boundaries of a natural preserve. walking trails run from…
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
Answer:
16 miles
Explanation:
Step1: Use parallelogram property
In a parallelogram, the diagonals bisect each other. So, $y + 2=2y - 3$.
Step2: Solve for y
Subtract y from both sides: $2=y - 3$. Then add 3 to both sides, getting $y = 5$.
Step3: Find length of one - half of a diagonal
Substitute $y = 5$ into $y + 2$, we get $5+2=7$. Substitute $y = 5$ into $3y - 4$, we get $3\times5-4=11$.
Step4: Calculate sum of trail lengths
The sum of the lengths of the two trails (the diagonals) is $2\times(7 + 1)=16$ miles.