Question

What is the perimeter of a parallelogram, if its area is 72 cm2 and the distances between the point of intersection of the diagonals and the sides are 3 cm and 4 cm?

Answer 1

Answer: 42 cm.

Step-by-step explanation:m

Given: The area of a parallelogram is 72 cm².

The distances between the point of intersection of the diagonals and the sides are 3 cm and 4 cm.

We know that the area of a parallelogram is given by :-

`Area=b*h`....................................................................(1), where b is the base and h is the corresponding height.

Since, the distance between point of intersection of the diagonals and the opposite sides are same.

Therefore,

`h_1=3+3=6\ cm\\h_2=4+4=8\ cm`

Now, putting the value of
`h_1=6\ cm` in (1). we get

`72=b_1*6\\\\\Rightarrow\ b_1=(72)/(6)=12`

⇒ The measure of one side =12 cm.

Now, putting the value of
`h_2=8\ cm` in (1). we get

`72=b_2*8\\\\\Rightarrow\ b_2=(72)/(8)=9`

⇒ The measure of second side = 9 cm.

Now,The perimeter of a parallelogram is given by :-

`2(b_1+b_2)\\=2(12+9)\\=2(21)=42\ cm`

Hence, the perimeter of a parallelogram = 42 cm.

Answer 2

The perimeter of a parallelogram is 42 cm.

Explanation:

The area of a parallelogram is 72 cm².

The formula for area of a parallelogram is

`A=base * height`

It is given that the distances between the point of intersection of the diagonals and the sides are 3 cm and 4 cm.

The distance between point of intersection of the diagonals and the opposite sides are same.

`h_1=3+3=6cm`

`A=b_1* h_1`

`72=b_1* 6`

`b_1=12cm`

The measure of a side is 12 cm.

`h_2=4+4=8cm`

`A=b_2* h_2`

`72=b_2* 8`

`b_2=9cm`

The measure of another side is 9 cm.

The perimeter of a parallelogram is

`P=2(b_1+b_2)=2(12+9)=42`

Therefore the perimeter of a parallelogram is 42 cm.