Final Answer:
The cost of laying grass in a triangular field of sides 50 and 65.65 meters at the rate of Rs. 7 per square meter is Rs. 7490. So none of the option given is correct.
Step-by-step explanation:
To find the cost of laying grass in a triangular field, we first need to calculate the area of the triangle in square meters and then multiply the area by the cost per square meter. In this case, the cost is given as Rs. 7 per square meter.
We are given two sides of the triangle: 50 meters and 65.65 meters. To find the area of the triangle, we would need the length of the third side if it's a scalene triangle, or if it is a right-angled triangle, we can use the two given sides as the base and height.
Since the problem doesn't specify otherwise, let's consider this triangle a right-angled triangle and assume that the side measuring 65.65 meters is the hypotenuse (the longest side of the right triangle, which is opposite the right angle).
This would make the 50 meter side one of the legs of the triangle, which we can consider as the base (or height, arbitrarily, due to the symmetry of the right triangle's properties concerning its legs).
The area of a right-angled triangle can be calculated using the formula: Area = (base * height) / 2.
Given one leg (base) as 50 meters, we need to find the other leg (height). We can do this using the Pythagorean theorem which is:
c^2 = a^2 + b^2
Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
Let's solve for the missing side (height):
(65.65)^2 = (50)^2 + b^2
4329.9225 = 2500 + b^2
4329.9225 - 2500 = b^2
1829.9225 = b^2
Taking the square root to find b:
b = sqrt(1829.9225)
b ≈ 42.78 meters
Now we can calculate the area of the triangle:
Area = (base * height) / 2
Area = (50 * 42.78) / 2
Area ≈ (2140) / 2
Area ≈ 1070 square meters
Next, we calculate the cost to lay grass on this area:
Total cost = area * cost per square meter
Total cost = 1070 * 7
Total cost = Rs. 7490
None of the given options (A. Rs. 2,275, B. Rs. 2,600, C. Rs. 2,975, D. Rs. 3,000) matches the result we calculated (Rs. 7490).
Therefore, there might be a mistake in the given options or in the assumption made about the nature of the triangle being a right-angled triangle.
If the triangle is not right-angled, this solution would not apply without knowing the length of the third side or other relevant angles.