In the accompanying diagram of parallelogram ABCD, diagonals AC and intersect BD at E, LaTeX: BE=2x B E = 2 x and LaTeX: ED=x+10.

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sarahsolana0210 sarahsolana0210

23-04-2018
Mathematics

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In the accompanying diagram of parallelogram ABCD, diagonals AC and intersect BD at E, LaTeX: BE=2x B E = 2 x and LaTeX: ED=x+10.

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Louli Louli · Answer 1 · 2018-04-23T16:14:31+02:00

Answer:
x = 10

Explanation:
In a parallelogram, diagonals bisect each other.

We are given that:
BD and AC are diagonals of a parallelogram
The two disgonals intersect at point E
BE = 2x
ED = x + 10

Now, based on the above, E bisects BD into two equal portions. This means that E is the midpoint of BD.
Therefore:
BE = ED
2x = x + 10
2x - x = 10
x = 10

We can check our solution:
BE = 2(10) = 20 units
ED = 10 + 10 = 20 units
They are equal

Hope this helps :)