Question

le 4: The perimeter of a rectangular field is 42m 28cm. The ratio of its length and breath is 5:2. Find the dimensions of the field.
Please explain ( :

​

Answer 1

Answer:

The length of the rectangular field is 15.1 m and breadth is 6.04 m

Step-by-step explanation:

Given :

The perimeter of a rectangular field is 42m 28cm.

The ratio of its length and breadth is 5:2

To find :

the dimensions of the field.

Solution :

The ratio of length and breadth is 5 : 2.

Let the length of the field be 5x and breadth be 2x.

The perimeter of the rectangular field

= 42 m 28 cm

= 42 m + 28 cm

= 42 m + 0.28 m ( 1 cm = 0.01 m )

= 42.28 m

We know,

Perimeter of the rectangle = 2(length + breadth)

42.28 = 2(5x + 2x)

42.28/2 = 7x

7x = 21.14

x = 21.14/7

x = 3.02

Length :

= 5(3.02)

= 15.1 m

Breadth :

= 2(3.02)

= 6.04 m

Therefore, the length of the rectangular field is 15.1 m and breadth is 6.04 m.

Answer 2

Length = 1510 cm

Breadth = 604 cm

Question -:

The perimeter of a rectangular field is 42m,28cm. The ratio of its length and breath is 5:2. Find the dimensions of the field.

Explanation -:

Given :

• Perimeter of a rectangular field = 42m,28cm
• Ratio of length and breadth = 5 : 2

To Find :

• Length and breadth of the rectangular field

Solution :

Ratio of length and breadth = 5 : 2

Let us assume the length as '5x' and breadth as '2x'

Perimeter of a rectangular field = 42m,28cm

42m + 28 cm

→ 4200cm + 28 cm (1 m = 100 cm)

→ (4200 + 28) cm

→ 4228 cm

Perimeter = 4228 cm

First we will calculate the length and breadth of the rectangular field

We know,

$\star \: \small\boxed{ \rm{ Perimeter \: of \: a \: rectangle = 2(Length + Breadth)}}$

On substituting the values we get

$\small\sf{ 4228 = 2(5x + 2x)}$

$\rightarrow \small\sf{4228 = 2(7x)}$

$\rightarrow \small\rm{ \dfrac{ \cancel{4228} \: \: 2114}{ \cancel{2}} = 7x}$

$\rightarrow\small\rm{2114 = 7x}$

$\rightarrow \small\rm{ \cancel\dfrac{2114}{7} = x }$

$\rightarrow \small\sf{x = 302}$

Length = 5x = 5 × 302 = 1510 cm

Breadth = 2x = 2 × 302 = 604 cm

$\rule{75mm}{2pt}$