The sides of a triangular farm are 20 m, 21 m and 29 m respectively. How much will be total expenses for cutting the crop at the rate of Rs. 15 per square meter ?

Question

Accepted Answer

To determine the total expenses for cutting the crop on the triangular farm, we first need to calculate the area of the triangle using Heron's formula. The sides of the triangle are given as 20 m, 21 m, and 29 m.

**Step 1: Calculate the semi-perimeter (s) of the triangle.**

The semi-perimeter $ s $ is calculated as follows:

$$ s = \frac{(a + b + c)}{2} $$

where $ a = 20 \, \text{m} $, $ b = 21 \, \text{m} $, and $ c = 29 \, \text{m} $.

$$ s = \frac{(20 + 21 + 29)}{2} = \frac{70}{2} = 35 \, \text{m} $$

**Step 2: Calculate the area (A) of the triangle using Heron's formula.**

Heron's formula for the area $ A $ is:

$$ A = \sqrt{s(s-a)(s-b)(s-c)} $$

Substitute the values:

$$ A = \sqrt{35(35-20)(35-21)(35-29)} $$

$$ A = \sqrt{35 \times 15 \times 14 \times 6} $$

$$ A = \sqrt{44100} $$

$$ A = 210 \, \text{square meters} $$

**Step 3: Calculate the total expenses for cutting the crop.**

The cost of cutting the crop is Rs. 15 per square meter. Therefore, the total expenses are:

$$ \text{Total Expenses} = \text{Area} \times \text{Rate per square meter} $$

$$ \text{Total Expenses} = 210 \times 15 = 3150 \, \text{Rs.} $$

Thus, the total expenses for cutting the crop are Rs. 3,150, which corresponds to Option 3.

**Explanation for Incorrect Options:**

- **Option 1 (Rs. 2,100):** This option is incorrect because it underestimates the total cost. The calculation of the area and the subsequent multiplication by the rate per square meter clearly shows that the expenses are higher than Rs. 2,100.

- **Option 2 (Rs. 1,890):** This option is incorrect as it also underestimates the total cost. The correct calculation yields a higher expense than Rs. 1,890.

- **Option 4 (Rs. 2,500):** This option is incorrect because it does not match the calculated total expenses. The correct calculation shows that the expenses are Rs. 3,150, which is higher than Rs. 2,500.

Therefore, based on the calculations and logical reasoning, Option 3 (Rs. 3,150) is the correct answer.