Question

The length of a rectangular field is 5: 3, and its area is 3.75 hectares. The fence for the land is Rs. 50/m. How much does it cost ?

Answer 1

In the above Question , th following information is given -

The ratio of the length and breadth of a rectangular field is 5: 3, and its area is 3.75 hectares.

The fence for the land is Rs. 50/m.

To find -

How much does it cost ?

Solution -

Here ,

The ratio of the length and breadth of a rectangular field is 5: 3,

So ,

Let us assume the following -

Let the length of the field be 5x metres and let the breadth be 3x metres .

Now ,

Area

=> Length × Breadth

=> 5x × 3x

=> 15 x² .

But ,

It's Area is 3.75 hectares .

Now ,

1 hectare = 10,000 m²

=> 3.75 hectares

=> 3.75 × 10000 m²

=> 37500 m²

So ,

15x ² = 37500

=> x² = 2500

=> x = 50 metres .

Now ,

Length

=> 5x

=> 5 × 50 m

=> 250 m

Breadth

=> 3x

=> 3 × 50 m

=> 150 m

Now ,

Perimeter of the field

=> 2 [ L + B ]

=> 2 [ 250 + 150 ]

=> 2 × 400

=> 800 metres .

Hence , the required perimeter of the field is 800 metres .

Now , the cost of the fence is Rs . 50 per metre

=> Cost -

=> Rs. 50 × 800

=> Rs. 40,000

Hence the land costs Rs. 40,000

______

Answer 2

$\huge\sf\pink{Answer}$

☞ Cost of Fencing = 40000

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ Ratio of Length and breadth = 5:3

✭ Area of the field = 3.75 hectare

✭ Cost of fencing = Rs 50 per meter

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

☆ The cost of fencing?

$\rule{110}1$

$\huge\sf\purple{Steps}$

✭ One Hectare = 1000 m²

So,

✭ 3.75 Hectare = 37500 m²

So then, Their Length and Breadth is, 5x and 3x

We know that the area of a rectanglecis given by,

$\underline{\boxed{\sf Area = Length × Breadth}}$

➝ $\sf 5x × 3x = 37500$

➝ $\sf 15x^2 = 37500$

➝ $\sf x = \frac{37500}{15}$

➝ $\sf\red{ x = 50 \ m}$

So now,

$\sf\bullet Length = 5×50 = 250 \ m$

$\sf\bullet Breadth = 3×50 = 150 \ m$

Now the Perimeter of the field is,

➳ $\sf Perimeter = 2(l+b)$

➳ $\sf Perimeter = 2( 250 + 150)$

➳ $\sf Perimeter = 2(400)$

➳ $\sf\green {Perimeter = 800 \ m }$

Cost of Fencing per meter is 50, So,

$\sf\dashrightarrow 800×50$

$\sf\orange{\dashrightarrow Cost = Rs\: 40000}$

$\rule{170}3$