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:

The perimeter of a parallelogram is 42 cm.

Step-by-step explanation:

The area of a parallelogram is 72 cm².

The formula for area of a parallelogram is

$A=base \times height$

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.

$h_1=3+3=6cm$

$A=b_1\times h_1$

$72=b_1\times 6$

$b_1=12cm$

The measure of a side is 12 cm.

$h_2=4+4=8cm$

$A=b_2\times h_2$

$72=b_2\times 8$

$b_2=9cm$

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.

Answer 2

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

$72=b_1*6\\\\\Rightarrow\ b_1=\frac{72}{6}=12$

⇒ The measure of one side =12 cm.

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

$72=b_2*8\\\\\Rightarrow\ b_2=\frac{72}{8}=9$

⇒ 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.