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. 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

Answer 1

Answer:

$16\ \text{miles}$

Step-by-step explanation:

In a parallelogram the diagnols bisect each other. So,

$DE=EB\\\Rightarrow y+2=3y-4\\\Rightarrow 4+2=3y-y\\\Rightarrow 6=2y\\\Rightarrow y=\dfrac{6}{2}\\\Rightarrow y=3$

$DE=y+2\\\Rightarrow DE=3+2\\\Rightarrow DE=5$

$BD=2DE\\\Rightarrow BD=2\times 5\\\Rightarrow BD=10$

$EC=2y-3\\\Rightarrow EC=2\times 3-3\\\Rightarrow EC=3$

$AC=2EC\\\Rightarrow AC=2\times 3\\\Rightarrow AC=6$

The sum of the diagonals is $BD+AC=10+6=16\ \text{miles}$

The sum of the lengths of the two trails is $16\ \text{miles}$.

Answer 2

Answer:

16  Miles

Step-by-step explanation:

Just took the quiz and got it right