Question

The area of a rectangular garden of length 40 m, is 1000 sqm. Find the breadth of the garden and its perimeter The garden is to be enclosed by 3 rounds of fencing, leaving an entrance of 4m. Find the cost of fencing the garden at a rate of 250 rupees per metre​

Answer 1

SOLUTION

Given that:

• The area of a rectangular garden of length 40 m, is 1000 sq. m.
• The garden is to be enclosed by 3 rounds of fencing, leaving an entrance of 4 m.
• The cost of fencing the garden at a rate of 250 rupees per metre.

To Find:

• The breadth of the garden and its perimeter.
• The cost of fencing the garden.

We know that:

• Area of a rectangle = Length × Breadth
• Perimeter of a rectangle = 2(Length + Breadth)

Let us assume:

• The breadth of the rectangular garden be x.

Find the breadth:

→ 40 × x = 1000

→ x = 1000/40

→ x = 25

Breadth of the rectangular garden = 25 m

Finding the perimeter:

• Perimeter = 2(40 + 25)
• Perimeter = 2 × 65
• Perimeter = 130

Perimeterof the rectangular garden = 130 m

Finding the length of three round of the garden, leaving an entrance of 4 m:

• Length to be fenced = 3 (130 - 4) m
• Length to be fenced = 3 × 126 m
• Length to be fenced = 378 m

Finding the cost of fencing the garden:

• Cost of 1 metre = Rs 250
• Cost of 378 metre = (250 × 378) = Rs 94500

The cost of fencing the garden = Rs 94,500

Answer 2

Question:-

• The area of a rectangular garden of length 40 m, is 1000 sqm. Find the breadth of the garden and its perimeter The garden is to be enclosed by 3 rounds of fencing, leaving an entrance of 4m. Find the cost of fencing the garden at a rate of 250 rupees per metre.

To Find:-

• Find the breadth of the garden and its perimeter.

• The cost of fencing of the garden.

Solution:-

• Let the breadth of the garden be ‘ x ’

First ,

We have to find the breadth:-

$\sf\longrightarrow \: Area = length \times breadth$

$\sf\longrightarrow \: 1000 = 40 \times x$

$\sf\longrightarrow \: 1000 = 40x$

$\sf\longrightarrow \: x = \cancel\dfrac { 1000 } { 40 }$

$\sf\longrightarrow \: x = 25$

Now ,

We have to find the perimeter:-

$\sf\longrightarrow \: Perimeter = 2( l + b )$

$\sf\longrightarrow \: Perimeter = 2( 40 + 25 )$

$\sf\longrightarrow \: Perimeter = 2( 65 )$

$\sf\longrightarrow \: Perimeter = 130$

Now ,

We have to find the length of fencing:-

$\sf\longrightarrow \: Length for fencing = 3( 130 - 4 )$

$\sf\longrightarrow \: Length for fencing = 3( 126 )$

$\sf\longrightarrow \: Length for fencing = 378 m$

Now ,

We have to find the cost of fencing:-

$\sf\longrightarrow \: Cost \: of \: meter = 250 ₹$

$\sf\longrightarrow \: Cost \: of \: 378 \: m = 250 \times 378$

$\sf\longrightarrow \: Cost = ₹ 94500$

Hence ,

• Cost is 94500