Question

A horse, a cow and a goat are tied, each by ropes of length 14 m, at the corners A, B and C respectively, of a grassy triangular field ABC with sides of lengths 35 m, 40 m and 50 m. Find the total area of grass field that can be grazed by them

Answer 1

Step 1: Problem Definition:
Each of the three animals grazes in a circular area with a radius of 14 m. The total grazed area is the sum of the individual areas.

Step 2: Area of a Circle Formula:
The area $A$ of a circle is calculated using the formula:\[A = \pi r^2\]where $r$ is the radius and $\pi$ is a constant (approximately 3.1416).

Step 3: Area per Animal:
With a radius of 14 m, the area grazed by one animal is:\[\text{Area grazed by one animal} = \pi (14)^2 = 196\pi \, \text{sq.m}\]Each animal grazes an area of $196\pi$ square meters.

Step 4: Total Grazed Area:
For three animals, the total grazed area is:\[\text{Total area grazed} = 3 \times 196\pi = 588\pi \, \text{sq.m}\]The combined grazed area for all three animals is $588\pi$ square meters.

Conclusion:
The total grazing area for the three animals is $588\pi$ square meters.