Question

3. The length and breadth of a rectangular field are in the
ratio 3:2. If the area of the field is 3456m2, find the
cost of fencing it at Rs 60 per metre.
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Answer 1

Step-by-step explanation:

Given:-

The length and breadth of a rectangular field are in the ratio 3:2. If the area of the field is 3456m^2,

To find:-

Find thecost of fencing it at Rs 60 per metre?

Solution:-

The ratio of the length and breadth of a rectangular field = 3:2

Let the length of the rectangular field be 3X m

Let the breadth of the rectangular field be 2X m

We know that

Area of a rectangle = length×breadth sq.units

Area of the rectangular field

=3X × 2X sq.m

=>6X^2 sq.m

According to the given problem

Area of the rectangular field = 3456 sq.m

=> 6X^2 = 3456

=>X^2 = 3456/6

=>X^2 = 576

=>X=√576

=>X=±24

X can not be negative ,since X is the length

X=24 m

3X = 3×24 = 72 m

2X=2×24 = 48 m

Length of the rectangular field = 72 m

Breadth of the rectangular field = 48 m

We know that

The Perimeter of a rectangle = 2(length+breadth) units

We have

length =72 m

Breadth = 48 m

Perimeter of the rectangular field

=2(72+48) m

=>2(120) m

=>240 m

Perimeter of the rectangular field = 240 m

The cost of fencing the rectangular field per 1 m

=Rs. 60

Total cost of fencing the given rectangular field

=240×60

=14400

Total cost = Rs. 14400

Answer:-

Total cost of fencing the given rectangular field

= Rs. 14400

Used formulae:-

• Area of a rectangle = length×breadth sq.units
• The Perimeter of a rectangle = 2(length+breadth) units