coolhabhi wrote:ABCD is a trapezium with AD & BC as parallel sides. E is a point on BC in such a way that ABED becomes a parallelogram. The ratio of the area of ABED to that of ABCD is
a) (AD + BC)/(AD + BE)
b) (AD + BE)/(AD + BC)
c) BE/BC
d) BC/BE
e) AD/BC
OE B
Let ABCD and ABED look as follows:
Area of parallelogram ABED = bh = (AD)(EF) = 2*1 = 2.
Area of trapezoid ABCD = (b� + b₂)/2 * h = (AD + BC)/2 * EF = (2+4)/2 * 1 = 3.
(ABED)/(ABCD) = 2/3. This is our target.
Now check the answer choices to see which yields our target of 2/3.
Only
B works:
(AD + BE)/(AD + BC) = (2 + 2)/(4 + 2) = 4/6 = 2/3.
The correct answer is
B.
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