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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 ...

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 ...

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1 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

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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