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very imp problem
Q)ABCD is a trapezium. AB and CD are parallel sides. Diagonals intersect at a point O.
If the area of the triangle CDO =q and Area of triangle ABO=p
Prove that area of trapezium =(root of p root of q) whole square
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triangle CDO / triangle APO = CD square / AB square
q/p = CD sq / AB sq
CD / AB = root q / root p
then, CD = root q and AB = root p
ar. of triangle ABO = 1/2bh
p = 1/2 root p.h
2p/root p = h
now, h = 2 root p
similarly, in triangle CDO
= 2 root q
now, ar. of trapezium ABCD = 1/2h(a+b)
= 1/2(2 root p + 2 root q)( root p + root q)
= (root p + root q )square
q/p = CD sq / AB sq
CD / AB = root q / root p
then, CD = root q and AB = root p
ar. of triangle ABO = 1/2bh
p = 1/2 root p.h
2p/root p = h
now, h = 2 root p
similarly, in triangle CDO
= 2 root q
now, ar. of trapezium ABCD = 1/2h(a+b)
= 1/2(2 root p + 2 root q)( root p + root q)
= (root p + root q )square
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