Question

The cost of cultivating a rectangular field at ₹35 per square metre is ₹71400. If the width of the field is 40m,find its length. Also,find the cost of fencing the field ai ₹50 per metre

Answer 1

Given:

The cost of cultivating a rectangular field at ₹35 per square metre is ₹71400. Also, the width of the field is 40m.

To find:

The width of the field and the cost of fencing the field at ₹50 per metre.

Solution:

As given,

we have,

The cost of cultivating one square metre area of a rectangular field = ₹35

This means,

In ₹1, the area of a rectangular field that is cultivated

$= \frac{1}{35} {m}^{2}$

So, in ₹71400, the area of a rectangular field that is cultivated

$= \frac{71400}{35} {m}^{2}$

$= 2040 {m}^{2}$

which is the area of a rectangular field.

Now,

Width of a rectangular field = 40 m

So,

$area \: of \: rectangle = length \: \times width$

$2040 = length \times 40$

$length = \frac{2040}{40}$

$= 51m$

Now,

The perimeter of a rectangular field

= 2 ( length + breadth)

= 2 ( 51 + 40 )

= 2 (91)

= 182 m

Now,

the cost of fencing one metre of field = ₹50

So, the cost of fencing 182 m of field

$= 50 \times 182$

$= ₹9100 \:$

Hence, the length of a rectangular field is 51 m and the cost of fencing the field at ₹50 per metre is ₹9100.

Answer 2

Given: The cost of cultivating a rectangular field at ₹35 per square metre is ₹71400. If the width of the field is 40m.

To find: The length and the cost of fencing the field ai ₹50 per metre.

Solution:

To calculate the cost of cultivating the entire field the cost per square metre must be multiplied by the area of the rectangular field.

$Cost = 35 * area$

But the area of the rectangular field can be calculated using the formula as shown below.

$area = length * width$

        $= length * 40m$

Also, the cost of cultivating the field at ₹35 per square metre is given as ₹71400. Now, the cost can be written as follows.

$Cost = 35*length*40$

$71400 = 35*length*40$

$length = 51 m$

In order to find the cost of fencing the field at ₹50 per metre, the perimeter of the field must be multiplied by 50.

$perimeter = 2(l+b)$

                 $= 2(51+40)$

                 $= 182 m$

$Cost = 182*50$

        $=9100$

Therefore, the length is 51 m and the cost of fencing the field ai ₹50 per metre is ₹9100.