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A horse is tied to at one corner of a square field with the rope and it can graze only 38.5% of the total area of the field. If the total cost of fencing the field at the rate of Rs. 15 per meter is Rs. 1200, then what is the length of the rope?

A horse is tied to at one corner of a square field with the rope and it can graze only 38.5% of the total area of the field. If the total cost of fencing the field at the rate of Rs. 15 per meter is Rs. 1200, then what is the length of the rope? Correct Answer 14 meters

GIVEN:

The horse can graze only 38.5% of total area of the field.

Total cost of fencing the field at the rate of Rs. 15 per meter is Rs. 1200

CONCEPT:

Application of formula for Perimeter and Area of square field.

And

The area grazed by the horse from the field will be equal to area of a quarter circle whose radius is equal to length of the rope.

FORMULA USED:

Perimeter of the square = 4 × Side of square

Area of square = Side2

CALCULATION:

According to the question:

Perimeter of the square field = 1200/15 = 80 m

So,

Length of a side of the square field = 80/4 = 20 m

Area of the field = 102 = 100 square meters

So,

Area grazed by horse = 38.5% of 400 = 154 m2

Suppose the length of the rope = r meters

So,

(1/4) × (22/7) × r2 = 154

⇒ r2 = 196

⇒ r = 14

So, length of the rope = 14 meter

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