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Mazyrski [523]
3 years ago
10

What is the perimeter of a parallelogram, if its area is 72 cm2 and the distances between the point of intersection of the diago

nals and the sides are 3 cm and 4 cm?

Mathematics
2 answers:
netineya [11]3 years ago
4 0

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.

GaryK [48]3 years ago
4 0

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.

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