Question

if the length and breadth of a rectangular field are in the ratio 6:4. find the length and breadth if the cost of fencing the field at the rate of Rs 80 per metre is Rs16000?​

Answer 1

Step-by-step explanation:

Given :-

the length and breadth of a rectangular field are in the ratio 6:4.

To find :-

Find the length and breadth if the cost of fencing the field at the rate of Rs 80 per metre is Rs16000?

Solution :-

The ratio of the length and breadth of the rectangular field = 6:4

Let they be 6X m and 4X m

Let the length of the rectangular field = 6X m

Let the breadth of the rectangular field = 4X m

Perimeter of a rectangle = 2(l+b) units

Perimeter of the given rectangular field

= 2(6X+4X) m

=> 2(10X) m

=> Perimeter = 20X m ------(1)

The total cost of fencing the field at the rate of Rs. 80 per 1 metre = Rs. 16000

Perimeter = Total Cost of fencing / Rate of 1 m

=> 16000/80

=> 200 m

So,

Perimeter of the rectangular field = 200 m----(2)

(1)&(2) are same since they are Perimeters

=> 20X = 200

=> X = 200/20

=> X = 10 m

Now, 6X = 6×10 = 60 m

and , 4X = 4×10 = 40 m

Answer:-

The length of the rectangular field = 60 m

The breadth of the rectangular field = 40 m

Check :-

Length = 60 m

Breadth = 40 m

Ratio = 60:40 = 6:4

and

Perimeter = 2(60+40)

=> P = 2(100)

=> P = 200 m

Cost of fencing the field per 1m = Rs. 80

Total cost of fencing the field of 200 m

=> 200×80

=> Rs. 16000

Verified the given relations in the given problem.

Used formulae:-

• Perimeter of a rectangle = 2(l+b) units

Where , l = length and b = breadth