Question

the cost of cultivating a rectangle field at ₹35 per square meters is ₹71400.if the width of the field is 49m find its length. also find the cost of fencing the field at ₹50 per metre.?​

Answer 1

Answer:

area of field

=71400/35

=2040

area=49*l =2040

=l = 2040/49

=41.63 (app) m

fencing field

=2(l*b)

=2(49*41.63)

=2*2040

=4080 m

Answer 2

$\large\underline{\bold{Given \:Question - }}$

• The cost of cultivating a rectangle field at ₹35 per square meters is ₹71400. If the width of the field is 49m, find its length. Also, find the cost of fencing the field at ₹50 per metre.

$\large\underline{\bold{Solution-}}$

Formula Used :-

$(1). \: \boxed{ \bf{Area_{(rectangle)} = Length \times Breadth }}$

$(2). \: \boxed{ \bf{Perimeter_{(rectangle)} = 2(Length + Breadth)}}$

Let do the problem now!!

Given :-

• The cost of cultivating a rectangle field at ₹35 per square meters is ₹71400.

• The width of the rectangle field is 49m.

To find :-

• Length of rectanglefield.

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

Now,

It is given that,

$\sf \: ₹ 35 \: is \: cost \: of \: cultivating \: area = 1 \: {m}^{2}$

$\sf \: ₹ 1 \: is \: cost \: of \: cultivating \: area = \dfrac{1}{35} \: {m}^{2}$

$\sf \: ₹ 71400 \: is \: cost \: of \: cultivating \: area = \dfrac{1}{35} \times 71400 = 2040 {m}^{2}$

So,

$\sf \: Cultivating \: area \: = \: 2040 \: {m}^{2}$

It implies,

$\sf \: Area_{(rectangle \: field)} \: = \: 2040 \: {m}^{2}$

Now,

• Breadth of rectangle field = 49 m

So,

$\sf \: Area_{(rectangle)} = Length \times Breadth$

$\sf \: 2040 = Length \times 49$

$\bf \: \therefore \: Length = \dfrac{2040}{49} m$

Now, to find the cost of fencing the field, we have to first find the Perimeter of field.

So,

$\sf \: Perimeter_{(rectangle \: field)} = 2(Length + Breadth)$

$\sf \: Perimeter_{(rectangle \: field)} = 2 \bigg(\dfrac{2040}{49} + 49 \bigg)$

$\sf \: Perimeter_{(rectangle \: field)} = 2\bigg( \dfrac{2049 + 2401}{49} \bigg)$

$\sf \: Perimeter_{(rectangle \: field)} = 2 \times \dfrac{4450}{49}$

$\bf \: \therefore \: Perimeter_{(rectangle \: field)} = \dfrac{8900}{49} \: m$

Now,

Given that

$\sf \: Cost \: of \: fencing \: 1 \: m \: = \: ₹ \: 50$

So,

$\sf \: Cost \: of \: fencing \: \dfrac{8900}{49} \: m = \dfrac{8900}{49} \times 50 = ₹ \: 9081.63 \: (approx.)$

Additional Information :-

Rectangle Properties

• A rectangle is a quadrilateral

• The opposite sides are parallel and equal to each other.

• Each interior angle is equal to 90°.

• The sum of all the interior angles is equal to 360°.

• Diagonals are of the same length.

• The diagonals bisect each other at different angles. One is acute, and another one is an obtuse angle.