In a square field labeled ABCD, with each side measuring 30 meters, lush grass covers the ground, enclosed by iron wires. Four cows, Red, Black, White, and Brown, are tethered by ropes at the corners A, B, C, and D respectively of the square field. Each rope has a length of 14 meters. The cows are restricted to grazing only within the confines of the square field. (Use π = 22/7)Q 116. If a 5th cow is tethered at the center of the square field and does not graze within the area of the four cows, what could be the maximum length (in integer meters) of the rope for the 5th cow? (Use √2 = 1.414)a) 5b) 6c) 7d) 8
Question
In a square field labeled ABCD, with each side measuring 30 meters, lush grass covers the ground, enclosed by iron wires. Four cows, Red, Black, White, and Brown, are tethered by ropes at the corners A, B, C, and D respectively of the square field. Each rope has a length of 14 meters. The cows are restricted to grazing only within the confines of the square field. (Use π = 22/7)Q 116. If a 5th cow is tethered at the center of the square field and does not graze within the area of the four cows, what could be the maximum length (in integer meters) of the rope for the 5th cow? (Use √2 = 1.414)a) 5b) 6c) 7d) 8
Solution
To solve this problem, we first need to find the distance from the center of the square to any of its corners. This is the diagonal of the square, which can be found using the Pythagorean theorem:
The length of the diagonal = √(side^2 + side^2) = √(30^2 + 30^2) = √1800 = 30√2 meters.
Since the diagonal of a square divides it into two equal right-angled triangles, the length from the center of the square to a corner is half the length of the diagonal. So, the distance from the center to a corner = 30√2 / 2 = 15√2 meters.
Now, the cows tethered at the corners can graze in a circular area with a radius of 14 meters. The distance from the center to the edge of this circular area along the diagonal is the radius of the circle subtracted from half the length of the diagonal, which is 15√2 - 14 = √2 meters.
Since √2 is approximately 1.414, the maximum length of the rope for the 5th cow, in integer meters, is 1 meter. However, this option is not given in the choices. The question might have a mistake or we might need to consider the rope length to the sides of the square instead of the corners.
If we consider the distance to the sides, the maximum length of the rope for the 5th cow would be half the side length of the square minus the radius of the circular area the corner cows can graze, which is 30/2 - 14 = 1 meter. Again, this option is not given in the choices.
Therefore, there seems to be a mistake in the question or the given choices.
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