Question

The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m, and 120 m (see figure below). The advertisements yield an earning of ₹ 5000 per m² per year. A company hired one of its walls for 3 months. How much rent did it pay?

Answer 1

We are given a triangular wall with the sides 122 m, 22 m, and 120 m. The company rented one of the walls for 3 months. The earnings from the advertisement are ₹5000 per m² per year. We need to calculate the rent paid by the company for 3 months.

Step-by-Step Solution:

1. Calculate the Area of the Triangle:

We can calculate the area of the triangle using **Heron's Formula**. The formula is: \[ A = \sqrt{s(s - a)(s - b)(s - c)} \] where: - \( a = 122 \, \text{m} \), - \( b = 22 \, \text{m} \), - \( c = 120 \, \text{m} \), - \( s \) is the semi-perimeter given by: \[ s = \frac{a + b + c}{2} = \frac{122 + 22 + 120}{2} = 132 \, \text{m} \] Now, substituting the values into Heron's formula: \[ A = \sqrt{132(132 - 122)(132 - 22)(132 - 120)} \] Simplifying: \[ A = \sqrt{132 \times 10 \times 110 \times 12} = \sqrt{1746240} = 1319.6 \, \text{m}^2 \]

2. Calculate the Rent for 3 Months:

The company earns ₹5000 per m² per year, so the total annual rent is: \[ \text{Annual Rent} = 5000 \times 1319.6 = 6598000 \, \text{₹} \] Since the company rented the wall for 3 months, the rent for 3 months is: \[ \text{Rent for 3 months} = \frac{6598000}{12} \times 3 = 1649500 \, \text{₹} \]

Final Answer:

The rent the company paid for 3 months is ₹ \(\boxed{16,49,500}\).