A square park is surrounded by a path of uniform width 2 meters all around it. The area of the path is 288 sq. meters. Find the perimeter of the park.

The answer is 136 m, and here’s why it is correct:

Let's break down the problem:

    
1. Let the side length of the square park be s meters.
    
2. The path surrounds the park with a uniform width of 2 meters, meaning the total side length (including the path) becomes s + 4 meters (2 meters on each side).
    
3. The area of the larger square, which includes the park and the path, can be calculated as: (s + 4)^2.
    
4. The area of the park itself is: s^2.
    
5. The area of the path is the difference between these two areas: (s + 4)^2 - s^2.

Setting up the equation for the area of the path given as 288 sq. meters:

(s + 4)^2 - s^2 = 288

Expanding this gives:

(s^2 + 8s + 16) - s^2 = 288

8s + 16 = 288

8s = 272

s = 34 meters

Now, to find the perimeter of the park, we use the formula for the perimeter of a square:

Perimeter = 4 * side length

So, the perimeter becomes:

4 * 34 = 136 meters

Thus, the final answer is indeed 136 m, as it represents the perimeter of the park.

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