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A rectangular field is 16 m long and 10 m wide. There is a path of uniform width all around it, having an area of 120 m². Find the width of the path.

Answer :

Final answer:

To find the width of the path, subtract the area of the field from the total area including the path. The width of the path is approximately 4.444m.

Explanation:

To find the width of the path, we need to subtract the area of the rectangular field from the total area including the path. The total area can be found by adding the area of the field and the area of the path:

Total area = field area + path area

We are given that the field is 16m long and 10m wide, so the field area is 16m * 10m = 160m². We are also given that the path area is 120cm². To convert the path area to square meters, we divide by 10,000 (since 1m = 100cm), resulting in 0.012m².

Now we can substitute these values into the equation:

Total area = 160m² + 0.012m² = 160.012m²

Since the total area includes the path, which has a uniform width all around the field, we can divide the total area by the length and width of the field to find the width of the path:

Width of path = total area / (length + 2 * width)

Substituting the values:

Width of path = 160.012m² / (16m + 2 * 10m) = 160.012m² / 36m = 4.444m

Therefore, the width of the path is approximately 4.444m.

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