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Question

# The parallel sides of a trapezium are x and y in length. The length of the line segement joining the mid points of the non parallel sides is

A
x+y2
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B
x+y
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C
2x+3y2
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D
xy2
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Solution

## The correct option is A x+y2Consider the given tapezium, Area of trapezium EFDC=(FE+x).h2 …..(1) Area of trapezium ABEF=12.(FE+y).h2 ….(2) Area of trapezium,ABCD=12.(x+y).h …..(3) (1)+(2)=(3) ⇒12.(FE+x).h2+12(FE+y).h2=12(x+y).h ⇒h2.FE+14h.(x+y)=12(x+y)h ⇒h2.FE=14.h(x+y) ⇒FE=x+y2 Hence, this is the answer.

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