Final answer:
The cost of laying grass in a triangular field with sides of 50m, 65m, and 65m is Rs.10500, calculated using Heron's formula to find the area and then multiplying by the rate of Rs.7 per m².
Step-by-step explanation:
The question asks to find the cost of laying grass in a triangular field with sides of 50m, 65m, and 65m, given the rate is Rs.7 per m². To find the cost, we first need to calculate the area of the triangle using Heron's formula since we have the lengths of all three sides.
Heron's formula states that the area of a triangle whose sides have lengths a, b, and c is √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter of the triangle, or (a+b+c)/2. For our triangle, the semi-perimeter s is (50+65+65)/2 = 90m.
Plugging the values into the formula, the area A is √(90(90-50)(90-65)(90-65)) = √(90*40*25*25) m². Simplifying this gives us the area as √(2250000) m², which equals 1500 m².
Finally, to find the cost, we multiply the area by the rate: Total Cost = Area × Rate = 1500 m² × Rs.7 per m² = Rs.10500.
Therefore, the cost of laying grass on the triangular field is Rs.10500.