Question

the side of a quadrilateral are in the ratio of 1:2:3:4 and its perimeter is 40 cm . find the length of each side

Answer 1

Given:

The sides of a quadrilateral are in the ratio 1:2:3:4

To find:

Each side of the quadrilateral

Now,

Let the sides be 1x cm, 2x cm, 3x cm, 4x cm

Also given that,

The perimeter of the quadrilateral is 40cm

so,

⇒ 1x + 2x + 3x + 4x = 40

⇒ 10x = 40

⇒ x = 40 ÷ 10

[Transporting 10 to RHS]

⇒ x = 4

So, the value of x is 4

Now,

Each side are

1x = 1*4 = 4 cm

2x = 2*4 = 8 cm

3x = 3*4 = 12 cm

4x = 4*4 = 16 cm

Hence,

The all four side of the quadrilateral is 4 cm, 8 cm, 12 cm and 16 cm.

- - -

Verifications,

The sum of the all four sides

= 4 + 8 + 12 + 16

= 12 + 12 + 16

= 24 + 16

= 40 cm as given in the question(perimeter of the quadrilateral)

Answer 2

To Find :

• we have to find the length of each side of quadrilateral.

Solution :

• Ratio of sides of quadrilateral 1:2 :3 :4
• Perimeter of quadrilateral = 40cm

$\purple{\textrm{perimeter of quadrilateral = sum of all four sides }}$

Let the sides of quadrilateral are x , 2x , 3x and 4x.

x + 2x + 3x + 4x = 40

10x = 40

x = 40/10

x = 4

So,

x = 4

2x = 2 × 4 = 8

3x = 3 × 4 = 12

4x = 4 × 4 = 16

$\large\dag \large { \red{\underline{\bf{Hence }}}}$

$\pink{\textrm{ Length of each side of quadrilateral is 4cm ,}}$$\pink{\textrm{8cm, 12cm and 16cm}}$

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