Question

What is the perimeter of a parallelogram, if its area is 24 cm2 and and the distances between the point of intersection of the diagonals and the sides are 2 cm and 3 cm?

Answer 1

p=20cm

Explanation:

Area of parallelogram is :
`24cm^(2)`

Since, it is a parallelogram, the four triangles are created by drawing diagonals of equal area=
`(24)/(4)=6cm^(2)`.

Now, Height of the one triangle is 2cm and the other is 3 cm.

Therefore, From ΔODC,

Area=
`(1)/(2){*}b_(1){*}h_(1)`

`6`=
`(1)/(2){*}b_(1){*}2`

`b_(1)=6`

`DC=6cm`

Again, from ΔOAD,

Area=
`(1)/(2){*}b_(2){*}h_(2)`

`6=(1)/(2){*}b_(2){*}3`

`b_(2)=4cm`

`AD=4cm`

Now, opposite sides of parallelogram are equal, therefore,AD=BC=4cm and DC=AB=6cm.

Perimeter of parallelogram= Sum of all the sides

=AB+BC+CD+AD

=6+4+6+4

=20cm