joeyesq10
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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 :

abiolataiwo2015

TheThe  sum of the lengths of the two trails is: C. 16 miles.

Sum of the length

AC and BD=diagonals of the parallelogram ABCD

DE=BE

AE=CE

Since DE=BE

Hence,

y+2=3y-4

Collect like term

2y=6

Divide both side by 2y

y=6/3

y=3

BD = y+2+3y-4

BD=3+2+3(3)-4

BD=3+2+9-4

BD=10 miles

Since,

y=3 miles and AE=CE

So,

AC=2CE

AC=2(2y-3)

AC=2[2(3)-3]

AC=2(6-3)

AC=6 miles

Sum of the lengths of the two trails:

Sum of the lengths=AC+BD

Sum of the lengths=10+6

Sum of the lengths=16 miles

Therefore the  sum of the lengths of the two trails is: C. 16 miles.

Learn more about   sum of the lengths here:https://brainly.com/question/123884

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