The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m, 15 m. The advertisements yield and earing of Rs. 2000 per `m^(2)` a year. A company hired one of its walls for 6 months. How much rent did it pay ?

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Calculate the semi-perimeter of the triangle
The sides of the triangle are given as \( a = 13 \, m \), \( b = 14 \, m \), and \( c = 15 \, m \).

The semi-perimeter \( s \) is calculated using the formula:
\[ s = \frac{a + b + c}{2} \]
Substituting the values:
\[ s = \frac{13 + 14 + 15}{2} = \frac{42}{2} = 21 \, m \]

### Step 2: Calculate the area of the triangle using Heron's formula
Heron's formula for the area \( A \) of a triangle is:
\[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
Substituting the values:
\[ A = \sqrt{21(21-13)(21-14)(21-15)} \]
Calculating each term:
\[ A = \sqrt{21 \times 8 \times 7 \times 6} \]
Calculating \( 21 \times 8 = 168 \), \( 7 \times 6 = 42 \):
\[ A = \sqrt{168 \times 42} \]
Calculating \( 168 \times 42 = 7056 \):
\[ A = \sqrt{7056} \]
Calculating the square root:
\[ A = 84 \, m^2 \]

### Step 3: Calculate the total earnings from advertisements for one year
The earnings per square meter per year are given as Rs. 2000. Therefore, the total earnings for the entire area for one year is:
\[ \text{Total Earnings} = A \times \text{Rate per m}^2 \]
Substituting the values:
\[ \text{Total Earnings} = 84 \times 2000 = 168000 \, \text{Rs.} \]

### Step 4: Calculate the rent for 6 months
Since the company hired the wall for 6 months, which is half a year, the rent paid will be:
\[ \text{Rent for 6 months} = \frac{\text{Total Earnings}}{2} \]
Substituting the values:
\[ \text{Rent for 6 months} = \frac{168000}{2} = 84000 \, \text{Rs.} \]

### Final Answer
The rent paid by the company for hiring the wall for 6 months is **Rs. 84000**.

---