A rectangular lawn 70 m by 50 m has two roads, each 5 m wide, running through its middle, one parallel to its length and the other parallel to its breadth. Find the cost of constructing the roads at Rs.120 per `m^(2)`.

Answer

To solve the problem step by step, we will calculate the area of the roads and then determine the cost of constructing them.

### Step 1: Calculate the area of the first road
The first road runs parallel to the breadth of the lawn.
- Length of the road = 50 m (width of the lawn)
- Width of the road = 5 m

**Area of Road 1 = Length × Width = 50 m × 5 m = 250 m²**

### Step 2: Calculate the area of the second road
The second road runs parallel to the length of the lawn.
- Length of the road = 70 m (length of the lawn)
- Width of the road = 5 m

**Area of Road 2 = Length × Width = 70 m × 5 m = 350 m²**

### Step 3: Calculate the area of the overlapping section
Both roads overlap in the center, forming a square.
- Side of the square = 5 m (width of each road)

**Area of the overlapping square = Side × Side = 5 m × 5 m = 25 m²**

### Step 4: Calculate the total area of the roads
To find the total area of the roads, we need to add the areas of both roads and subtract the area of the overlapping section.

**Total Area of Roads = Area of Road 1 + Area of Road 2 - Area of Overlapping Square**
- Total Area = 250 m² + 350 m² - 25 m²
- Total Area = 600 m² - 25 m² = 575 m²

### Step 5: Calculate the cost of constructing the roads
The cost of constructing the roads is given as Rs. 120 per m².

**Total Cost = Total Area × Cost per m²**
- Total Cost = 575 m² × 120 Rs/m²
- Total Cost = 69000 Rs

### Final Answer
The cost of constructing the roads is Rs. 69,000.

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