2. Mukul Raj is a social worker. In his village, there was no school building. Mukul donated a rectangular plot of land for a school building. The dimensions of the plot are in the ratio 10:3. He also donated ₹15,600 to fence the plot at ₹50 per meter. (a) What are the dimensions of the plot? (b) Find the area of the plot. (c) Which value does Mukul Raj depict?
Answer (1)
This problem involves geometry and simple algebra.
Let's break down the solution step-by-step:
Given Information:
The dimensions of the rectangular plot are in the ratio 10:3.
Mukul donated ₹15,600 to fence the plot at ₹50 per meter.
(a) What are the dimensions of the plot?
To find the dimensions, let's denote the length and width of the plot as:
Length = 10 x
Width = 3 x
The cost of fencing the plot is given by the perimeter multiplied by the cost per meter:
2 × ( 10 x + 3 x ) × 50 = 15 , 600
This simplifies to:
2 × 13 x × 50 = 15 , 600
1300 x = 15 , 600
Solve for x :
x = 1300 15 , 600 = 12
Therefore, the dimensions of the plot are:
Length = 10 x = 10 × 12 = 120 meters
Width = 3 x = 3 × 12 = 36 meters
(b) Find the area of the plot.
The area of a rectangle is given by:
Area = Length × Width = 120 × 36 = 4320 square meters
(c) Which value does Mukul Raj depict?
Mukul Raj demonstrates the values of generosity and community service by donating land and funds to facilitate the building of a school in his village. His actions reflect a strong sense of social responsibility and a commitment to improving the education infrastructure for the benefit of the community.
