Question

Diagonals EG and FH of a parallelogram EFGH intersect each other at O. If OE = 3 cm and OH = 2 cm, determine the length of EG and FH.​

Answer 1

$\sf \pink{ \tt{SOLUTION:–}}$

$\sf \red{ \tt \implies{Here \: {\fbox{O }}\: is \: mid \: point \: of \: diagnols}}$

In triangle EFG,

OF is the median.

Therefore area(△EOF)=area(△GOF) (since median of a triangle divides the triangle into two triangles of equal area)––––(1)

In triangle FGH,

GO is the median.

Therefore, area(△HOG)=area(△GOF) (reason same as above)––––(2)

And in Triangle EHG,

HO is the median.

Therefore, area(△EOH)=area(△HOG) (reason same as above)––––(3)

From eq 1 , 2 and 3 it can be concluded that

ar(ΔGOF)=ar(ΔEOH)=ar(ΔGOH)=ar(ΔEOF)

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