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

16 Miles

Explanation:

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Answer 2

`16\ \text{miles}`

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=(6)/(2)\\\Rightarrow y=3`

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

`BD=2DE\\\Rightarrow BD=2* 5\\\Rightarrow BD=10`

`EC=2y-3\\\Rightarrow EC=2* 3-3\\\Rightarrow EC=3`

`AC=2EC\\\Rightarrow AC=2* 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}`.