The inner rectangular garden has a length of 23 m and a width of 17 m. Using the standard area formula for a rectangle, Area = length × breadth, we calculate 23 × 17 = 391 m².

A rectangular garden is 23 m long and 17 m wide. A path 2.5 m wide runs all around the outside of the garden. Find the area of the path.

Answer: The area of the path is $225\text{ m}^2$ .

Step-by-step solution

Step 1: Calculate the area of the inner rectangular garden

The inner rectangular garden has a length of $23\text{ m}$ and a width of $17\text{ m}$ . Using the standard area formula for a rectangle, $\text{Area} = \text{length} \times \text{breadth}$ , we calculate $23 \times 17 = 391\text{ m}^2$ .

Step 2: Determine the outer dimensions including the path

Since the path has a uniform width of $2.5\text{ m}$ running all around the outside, we add twice the width of the path to both the length and the breadth. The outer length becomes $23 + 5 = 28\text{ m}$ and the outer breadth becomes $17 + 5 = 22\text{ m}$ .

Step 3: Calculate the area of the outer rectangle

Now, we find the total area enclosed by the outer boundary including the garden and the path. Multiplying the outer dimensions gives $28 \times 22 = 616\text{ m}^2$ .

Step 4: Calculate the area of the path

The area of the path alone is obtained by subtracting the inner garden area from the total outer area. Subtracting $391\text{ m}^2$ from $616\text{ m}^2$ yields $225\text{ m}^2$ .

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