Question

Find the perimeter of the parallelogram. 14. Two sides of a parallelogram are in the ratio 5 : 3 and its perimeter is 48 cm. Find the length of each of its sides.​

Answer 1

Step-by-step explanation:

$\huge\fbox\red{A}\fbox\orange{n}\fbox\purple{s}\fbox\green{w}\fbox\pink{e}\fbox\blue{r}$

Since 8*6 = 48 => one of the sides is the height as area parallelogram = Base * Height! This indicates the shape is really a rectangle. But let us see if this can be proved.

Consider any one diagonal which bisects the parallelogram into 2 equal halves.

The area of the triangle with the two adjacent sides and the diagonal

= 48/2 = 24 sq. cm

Area of this triangle = 1/2 absinC = 24

1/2 * 6 * 8 * SINC = 24

24 * SIN C = 24

SIN C = 1

C = 90 Degrees

This indicates that the said parallelogram is a rectangle and both diagonals are the same length

Diagonal length = sqrt(6² + 8²) = sqrt(36 + 64) = sqrt (100) = 10cm

Both Diagonals are 10cm long

Answer 2

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Given

Ratio = 5:3

Perimeter = 48 cm

To find

The length of the sides of the parallelogram

Solution

Let the adjacent sides be 5x and 3x

Now,

Perimeter of parallelogram = 2 ( L + B)

⛬ 48 = 2 ( 5x + 3x )

48 = 2 × 8x

$\green{8x = \frac{48}{2} = 24 }$

$\orange{x = \frac{24}{8} = 3}$

So,

L = 5x = 5 × 3 = 15cm

B = 3x = 3 × 3 = 9cm

We known that the opposite sides of a parallelogram are equal

hence, the length of all sides of the parallelogram will be 15 cm, 9cm , 15 and 9cm