Let's solve the problem step by step:
1. Identify the length and width of the park:
- The ratio of length to width is given as 3:1.
- Let the length of the park be [tex]\( L = 3x \)[/tex] and the width be [tex]\( W = x \)[/tex].
2. Use the perimeter to find [tex]\( x \)[/tex]:
- The perimeter of the rectangle is given by the formula [tex]\( 2(L + W) \)[/tex].
- Substituting the values, we get [tex]\( 2(3x + x) = 320 \)[/tex].
- Simplify this equation: [tex]\( 2 \times 4x = 320 \)[/tex] which gives [tex]\( 8x = 320 \)[/tex].
- Solving for [tex]\( x \)[/tex], we find [tex]\( x = 40 \)[/tex].
3. Calculate the actual length and width:
- Length [tex]\( L = 3x = 3 \times 40 = 120 \)[/tex] meters.
- Width [tex]\( W = x = 40 \)[/tex] meters.
4. Determine the dimensions of the inner rectangle:
- The path is 2 meters wide inside the boundary.
- The inner length is [tex]\( L_{\text{inner}} = L - 2 \times 2 = 120 - 4 = 116 \)[/tex] meters.
- The inner width is [tex]\( W_{\text{inner}} = W - 2 \times 2 = 40 - 4 = 36 \)[/tex] meters.
5. Calculate the areas:
- The outer area [tex]\( A_{\text{outer}} = L \times W = 120 \times 40 = 4800 \)[/tex] square meters.
- The inner area [tex]\( A_{\text{inner}} = L_{\text{inner}} \times W_{\text{inner}} = 116 \times 36 = 4176 \)[/tex] square meters.
6. Find the area of the path:
- The area of the path is the difference between the outer and inner areas.
- [tex]\( A_{\text{path}} = A_{\text{outer}} - A_{\text{inner}} = 4800 - 4176 = 624 \)[/tex] square meters.
7. Calculate the total cost of paving the path:
- The cost per square meter is ₹1.50.
- Therefore, the total cost [tex]\( \text{Total Cost} = A_{\text{path}} \times \text{cost per square meter} = 624 \times 1.50 = 936 \)[/tex] rupees.
So, the cost of paving the path inside the park is ₹936.
The correct answer is:
(a) ₹936/-
