Question

in a trapezium, the diagonals divide each other in the ratio of 1:3 Find the ratio of the parallel sides

Answer 1

Given :

For trapezium ,

The diagonal divides each other in ratio 1 : 3

To Find :

The ratio of parallel side

Solution :

From figure

ABCD is a Trapezium , with side AB , BD , DC , CA

The diagonal AD and BC bisect at O

i.e Diagonal BC divide the diagonal AD in ratio 1 : 2 at O

i.e   OA : OD = 1 : 2

In Triangle Δ AOB and Δ COD

∠  AOB = ∠COD                                                ( Vertically opposite angles )

∠  ABO =  ∠OCD                                                    ( Alternate angles )

∴  Δ AOB ≈ Δ COD                                                    ( AA similarity )

So,

$\dfrac{OA}{OD}$  = $\dfrac{AB}{CD}$

i.e  $\dfrac{1}{2}$ = $\dfrac{AB}{CD}$

∴     CD = 2 AB

Or,    CD : AB = 2 : 1

Hence, The ratio of parallel sides of Trapezium is 2 : 1   Answer