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WILL GIVE BRAINLIEST. Need an answer ASAP!

The diagonals of a rectangle ABCD intersect at E. AE = x+4 and CE = 3x-12. Find BE

WILL GIVE BRAINLIEST Need An Answer ASAP The Diagonals Of A Rectangle ABCD Intersect At E AE X4 And CE 3x12 Find BE class=

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Answer:

[tex]BE=12 units[/tex]

Step-by-step explanation:

[tex]We\ know\ that,\\In\ a\ rectangle\ all\ diagonals\ are\ equal\ and\ bisect\ each\ other.\\Hence,\\In\ Rectangle\ ABCD,\\AE=EC\\Hence,\\Substituting\ the\ values\ we\ get:\\x+4=3x-12\\Hence,\\-2x=-16\\x=\frac{-16}{-2}=8\\Now,\\We\ also\ know\ that,\\ AC=DB\\Hence,\\\frac{AC}{2}=\frac{DB}{2} \\Hence,\\DE=EB=AE=EC\\Hence,\\Since\ AE=BE,\\BE=x+4\\We\ already\ know\ that\ x=8.\\Hence, BE=8+4=12[/tex]

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