Question

11. In parallelogram ABCD, the diagonals bisect each other
at P so that PA=9cm,PC=x+ y, PB=x-y and PD=5cm. Find the
length of the diagonals.​

Answer 1

Given:

PA=9cm,

PC=x+ y,

PB=x-y and

PD=5cm

To find:

The length of the diagonals.

Solution:

1) The diagonals of the parallelogram divide it into similar triangles.

2) So by the rule of similarity, the ratio of the sides of the triangle must be given as:

• PA/PD = PC/PB

• 9/5 = x+y/x-y

by comparing we get x+y is 9 and x-y is 5.

3) The length of the diagonal

• AC = PA+PC

• AC = 9+x+y

• AC = 9+9

• AC = 18 cm.

and diagonal

• BD = PB+PD

• BD = 5+x-y

• BD = 5+5

• BD = 10cm.

The length of the diagonals is 18cm and 10 cm.