Question 1 Find the cost of laying grass in a triangular field of sides 50m, 65m and 65m at the rate of Rs.7 per m2.
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Solution
Given, ABC is a triangular field with sides AB = a = 50m, BC = b = 65m and CA = c = 65m.
∴Semi-perimeter of triangular field, s=a+b+c2 =50+65+652=1802=90m ∴Area of a triangle field =√s(s−a)(s−b)(s−c)[by Heron’s formula] =√90(90−50)(90−65)(90−65) =√90×40×25×25 =3×2×10×25 =6×250=1500m2 The cost of laying grass per 1 m2 = Rs.7 ∴ The cost of laying grass per 1500 m2 = 7 × 1500 = Rs.10500 Hence, the cost of laying grass in the triangular field is Rs.10500.