ABCD is a trapezium in which AB || DC and AB> CD. If EF is its median and X, Y are mid-points of its diagonals, then the value of root AB^2-CD^2 /EF.XY is
1/4
4
2
1/2
Answers
Given : ABCD is a trapezium in which AB || DC and AB > CD.
EF is its median and
X, Y are mid-points of its diagonals,
To Find : the value of (AB² -CD²)/(EF . XY)
Solution:
line joining the mid-point of two sides of a triangle is equal to half the length of the third side and parallel to 3rd side.
EF is its median
=> AB || CD || EF
EF = (1/2)(AB + CD)
X, Y are mid-points of its diagonals,
Hence EX = (1/2) CD EY = (1/2)AB
XY = EY - EX = (1/2)( AB - CD)
EF . XY = (1/2)(AB + CD) * (1/2)( AB - CD) = (1/4) (AB² -CD²)
=> 4 = (AB² -CD²)/(EF . XY)
Hence value of (AB² -CD²)/(EF . XY) is 4
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