Two crossroads, each of width 3 m, run at right angles through the centre of a rectangualr park of length 90 m and breadth 60 m and parallel to its sides. Find the area of the roads. Also find the cost of constructing the roads at the rate of 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 (length 90 m, width 3 m)
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]

For the first road:
- Length = 90 m
- Width = 3 m

Calculating the area:
\[ \text{Area of first road} = 90 \, \text{m} \times 3 \, \text{m} = 270 \, \text{m}^2 \]

### Step 2: Calculate the area of the second road (length 60 m, width 3 m)
For the second road:
- Length = 60 m
- Width = 3 m

Calculating the area:
\[ \text{Area of second road} = 60 \, \text{m} \times 3 \, \text{m} = 180 \, \text{m}^2 \]

### Step 3: Calculate the area of the overlapping square (width 3 m)
Since the two roads overlap at the center, we need to subtract the area of the overlapping square:
- Side of the square = 3 m

Calculating the area of the square:
\[ \text{Area of overlapping square} = 3 \, \text{m} \times 3 \, \text{m} = 9 \, \text{m}^2 \]

### Step 4: Calculate the total area of the roads
Now we can find the total area of the roads by adding the areas of the two roads and subtracting the area of the overlapping square:
\[ \text{Total area of roads} = \text{Area of first road} + \text{Area of second road} - \text{Area of overlapping square} \]
\[ \text{Total area of roads} = 270 \, \text{m}^2 + 180 \, \text{m}^2 - 9 \, \text{m}^2 \]
\[ \text{Total area of roads} = 441 \, \text{m}^2 \]

### Step 5: Calculate the cost of constructing the roads
The cost of constructing the roads is given at the rate of Rs 120 per m². Therefore, the total cost can be calculated as:
\[ \text{Cost} = \text{Total area of roads} \times \text{Cost per m}^2 \]
\[ \text{Cost} = 441 \, \text{m}^2 \times 120 \, \text{Rs/m}^2 \]
\[ \text{Cost} = 52920 \, \text{Rs} \]

### Final Answer
- The area of the roads is \( 441 \, \text{m}^2 \).
- The cost of constructing the roads is \( 52920 \, \text{Rs} \).