In the figure given below, ABCD is a parallelogram. E is a point on AB. CE intersects the diagonal BD at G and EF is parallel to BC. If AE : EB = 1 : 2 find (i) EF : AD
(ii) area of triangle BEF : area of triangle ABD [3] D C
F
G
A E B
Answers
Answered by
51
(I)EF:AD=2:3
(II)AREA OF TRIANGLE BEF:AREA OF TRIANGLE ABC=4:9
(II)AREA OF TRIANGLE BEF:AREA OF TRIANGLE ABC=4:9
Answered by
37
Answer:
(i)EF:AD=2:3
(ii)area of triangle BEF:area of triangle ABD
=4:9
Step-by-step explanation:
(i) In triangle BEF & triangle BAD
Triangle BEF is similar to Triangle BAD
(Basic Proportionality Theorem)
Therefore,
BE/AB=EF/AD=BF/BD
BE/AE+AB=EF/AD
We know that,
AE/EB=1/2
Therefore,
EF/AD=2/2+1
EF:AD=2:3
(ii)ar(Triangle BEF)/ar(Triangle BAD)
=Square of (EF/AD)
=2^2/3^2
=4/9
Therefore,
ar(Triangle BEF):ar(Triangle BAD)
=4:9
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