KVPY SA Exam 2013 Question Paper

Question : 9 of 80

Marks: +1, -0

In a rectangle ABCD, points X and Y are the midpoints of AD and DC, respectively. Lines BX and CD when extended intersect at E, lines BY and AD when extended intersect at F. If the area of ABCD is 60 then the area of BEF is

Validate

Solution:

Let AB = x
BC = y
xy = 60
ΔXED ≃ ΔXBA
and ΔDFY ≃ ΔCBY
ΔBEF = BXDY + ΔXED + ΔDFY + ΔDEF
= 60 + ΔDEF

60+1/2×xy

60 + 30 = 90

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