Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of Rs7 per m2.Also find the cost of fencing the field at the rate of Rs 9 per m
Question
Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of Rs7 per m2.Also find the cost of fencing the field at the rate of Rs 9 per m
Solution
To solve this problem, we need to find the area of the triangular field and the perimeter of the field.
Step 1: Find the area of the triangular field The given triangle is an isosceles triangle (two sides are equal). The formula to find the area of an isosceles triangle is √[s(s - a)(s - b)(s - c)], where s is the semi-perimeter of the triangle and a, b, c are the sides of the triangle.
First, let's find the semi-perimeter (s) of the triangle. s = (a + b + c) / 2 s = (50 + 65 + 65) / 2 s = 90 m
Now, let's find the area of the triangle. Area = √[s(s - a)(s - b)(s - c)] Area = √[90(90 - 50)(90 - 65)(90 - 65)] Area = √[904025*25] Area = 1500 m^2
Step 2: Find the cost of laying grass The cost of laying grass is Rs 7 per m^2. So, the total cost of laying grass is: Cost = Area * Rate Cost = 1500 m^2 * Rs 7/m^2 Cost = Rs 10500
Step 3: Find the cost of fencing the field The cost of fencing the field is Rs 9 per m. The total cost of fencing is equal to the perimeter of the field times the rate per meter. The perimeter of the field is the sum of all sides, which is 50 m + 65 m + 65 m = 180 m. Cost of fencing = Perimeter * Rate Cost of fencing = 180 m * Rs 9/m Cost of fencing = Rs 1620
So, the cost of laying grass in the field is Rs 10500 and the cost of fencing the field is Rs 1620.
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