A rectangular grassy plot is 112 m by 78 m. It has a gravel path 2.5 m wide all round it on the inside. Find the area of the path and the cost of constructing it at Rs. 2 per square metre.

Answer

To solve the problem step by step, we will find the area of the gravel path and then calculate the cost of constructing it.

### Step 1: Determine the dimensions of the outer rectangle
The dimensions of the grassy plot are given as:
- Length = 112 m
- Width = 78 m

Since the gravel path is 2.5 m wide all around the grassy plot, we need to add this width to both dimensions.

**Calculation:**
- New Length = 112 m + 2.5 m + 2.5 m = 112 m + 5 m = 117 m
- New Width = 78 m + 2.5 m + 2.5 m = 78 m + 5 m = 83 m

### Step 2: Calculate the area of the outer rectangle
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]

**Calculation:**
- Area of the outer rectangle = 117 m × 83 m = 9711 m²

### Step 3: Calculate the area of the inner rectangle (grassy plot)
Now we will calculate the area of the inner rectangle, which is the grassy plot.

**Calculation:**
- Area of the inner rectangle = 112 m × 78 m = 8736 m²

### Step 4: Calculate the area of the gravel path
The area of the path can be found by subtracting the area of the inner rectangle from the area of the outer rectangle.

**Calculation:**
- Area of the path = Area of outer rectangle - Area of inner rectangle
- Area of the path = 9711 m² - 8736 m² = 975 m²

### Step 5: Calculate the cost of constructing the path
The cost of constructing the path is given at Rs. 2 per square meter.

**Calculation:**
- Cost = Area of the path × Cost per square meter
- Cost = 975 m² × Rs. 2/m² = Rs. 1950

### Final Answer
The area of the path is 975 m², and the cost of constructing it is Rs. 1950.

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