Question

two sides of a parallelogram are in ratio 5:3 and it's perimeter is 48cm. Find the length of each sides​

Answer 1

The two sides are 15 cm and 9 cm

Explanation:

Let x be the longer side and y the shorter side

We are given x : y = 5:3

We can represent this as a fraction:

`(x)/(y) = (5)/(3)`

Multiplying both sides by y:

`(x)/(y) * y = (5)/(3) * y\\\\x = (5)/(3)y`

Perimeter of a parallelogram = 2(x + y)

We are given 2(x + y) = 48

Dividing both sides by 2 gives:
2(x + y)/2 = 48/2

x + y = 24

Substituting

`x = (5)/(3)y \text{ we get}\\\\\\(5)/(3)y + y = 24\\\\`

Multiplying throughout by 3 gest rid of the denominator

`(5)/(3)y \cdot 3 + y \cdot 3 = 24 \cdot 3\\\\\\\\\rightarrow 5y + 3y = 72\\\\\rightarrow 8y = 72\\\\\rightarrow y = (72)/(8) = 9\\`

Since

`x = (5)/(3) y\\\\x = (5)/(3) \cdot 9\\\\x = 15\\\\`

Therefore the two sides are 15 cm and 9 cm