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Hi Suru,
The ratio would be 4.
See consider the non parallel side of length 4, is cut by the parallel line into lengths x,y
So x+y = 4. We need to find x+y
Also the other non-parallel side would be divided in the same ratio (x/y).
So their lengths as cut by the paralledl line to the base would be kx,ky
So kx+ky = 6 or k(x+y) = 6.
Dividing k = 6/4 = 3/2
And the perimeters of the two trapezium are equal.
So x+kx+3+(length of parallel line) = y+ky+9+(length of parallel line)
So x(1+k) = 6+y(1+k)
Sub for k=3/2, we get 5x-5y=12. Solve with x+y=4.
We get x=3.2, y=0.8
So x/y = 4, and that is the ratio.
Best Regards,
Ashwin (IIT Madras).
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