The parallel sides of a trapezoid are 3 cm and 9cm. The non-parallel sides are 4 cm and 6 cm. A line parallel to the base divides the trapezoid into two trapezoids of equal perimeters. The ratio in which each of the non parallel sides is divided, if AP/BQ= PD/QC, is ...

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).