Question

The four sides of a quadrilateral are in the ratio 2 : 3 : 4 : 5. if the perimeter of the quadrilateral is 280 cm, find the length of the four sides.​

Answer 1

Given :

• Four sides of a quadrilateral are in the ratio 2 : 3 : 4 : 5
• Perimeter of the quadrilateral is 280 cm

To Find :

• The length of four sides.

Calculation :

Here, it's given that four sides of a quadrilateral are in the ratio 2 : 3 : 4 : 5 and perimeter of the quadrilateral is 280 cm. And we have to calculate the length of four sides. Firstly, let's assume the ratios of lengths of sides as,

• 2 = 2x
• 3 = 3x
• 4 = 4x
• 5 = 5x

Now as we know that,

$\boxed{ \tt{Sum \: of \: all \: sides = Perimeter}}$

So, by applying this formula, we will calculate the length of four sides of a quadrilateral.

$\implies \bf 2x + 3x + 4x + 5x = 280 \: cm$

• On adding the numbers,

$\implies \bf 14x = 280 \: cm$

• Transposing 14 to R.H.S and dividing 280 by 14

$\implies \bf x = \dfrac{280}{14}$

• On dividing the numbers,

$\implies\underline{\boxed{\bf{x = 20}}}$

Therefore, the value of x is 20.

According to the Question,

Now, let us calculate the length of four sides of a quadrilateral.

$\dag$ Length of first side :

$\longrightarrow$ 2x = 2 × 20

$\longrightarrow$ 40 cm

$\dag$ Length of second side :

$\longrightarrow$ 3x = 3 × 20

$\longrightarrow$ 60 cm

$\dag$ Length of third side :

$\longrightarrow$ 4x = 4 × 20

$\longrightarrow$ 80 cm

$\dag$ Length of fourth side :

$\longrightarrow$ 5x = 5 × 20

$\longrightarrow$ 100 cm

Therefore,

• The length of four sides are 40 cm, 60 cm, 80 cm and 100 cm.

Answer 2

Given : ↴

$\sf \: Four \: sides \: of \:a \: \: quadrilateral \: are \: in \: the \: ratio \: 2 : 3 \: : 4 : 5.$

$\sf \: Perimeter \: of \: the \: quadrilateral \: is \: 280 \: cm.$

To find : ↴

$\sf \: We \: have \: to \: find \: the \: length \: of \: the \: four \: sides.$

So, Let's Start : ↴

$\sf \: Let, \: the \: four \: sides \: of \: a \: quadrilateral \: be, 2x, \: 3x, \: 4x \: and \: 5x.$

$\sf \: \red{ It \: is \: Given \: that \: : }$

$\bf \sf \: The \: perimeter \: of \: the \: quadrilateral \: is \: 280 \: cm.$

$\sf \: As \: we \: know \: that \: Perimeter \: is \: equal \: to \: sum \: of \: all \: sides.$

$\sf \: So, \: 2x \: + \: 3x \: + \: 4x \: + \: 5x \: = \: 280 \: cm.$

$\sf \rightarrow \: 14x \: = \: 280 \: cm.$

$\sf \rightarrow \: x \: = \: \dfrac{280}{14}$

$\sf \red{So, \: the \: value \: of \: x \: is \: 20. }$

$\sf \: \underline{Hence \: the \: four \: sides \: of \: the \: quadrilateral \: are} \: :$

$\sf \longrightarrow \: 2x \: = \: 2 \times 20 \: = \: 40 \: cm$

$\sf \longrightarrow \: 3x \: = \: 3 \: \times \: 20 \: = \: 60 \: cm$

$\sf \longrightarrow \: 4x \: = \: 4 \: \times \: 20 \: = \: 80 \: cm$

$\sf \longrightarrow \: 5x \: = \: 5 \: \times \: 20 \: = \: 100 \: cm$

$\sf \therefore \: \underline{The\: length \:of \:four \:sides\: are\: }\::$ ↴

$\sf \longrightarrow \purple{40\: cm,\: 60 \:cm,\: 80 \:cm \:and \:100 \:cm.}$

$\sf \underline { Extra \: information }\::$ ↴

In quadrilateral 'quad' mean four and 'lateral' means sides. A quadrilateral is a closed figure made up of four segments. In other words it is a polygon with four sides. It has four sides, four vertex and four angles.