Answer :
Final answer:
To find the width of a path surrounding a rectangular field, we first calculate the total area of the field and the path. Then, we set up a quadratic equation using the total area and solve it for the width of the path.
Explanation:
To solve this problem, we first need to understand that the total area of the field and the path together is larger than just the area of the field. We also know that the path forms a uniform ring around the rectangular field.
Firstly, let's calculate the area of the rectangular field. The area of a rectangle is given by the formula: Area= length × width . Thus, the area of our field is 16m × 10m = 160m².
Next, we are given that the area of the path is 120m². So the combined area of the field and path must be 160m² + 120m² = 280m².
Now, we know that the path surrounds the field, in other words, it adds the same amount of width and length on each side of the rectangle. Let 'w' be the width of the path. So, the overall length and width of the rectangular field including the path will be 16m + 2w and 10m + 2w respectively.
Hence, the total area can also be rewritten as (16m + 2w) × (10m + 2w) = 280m².
Solving this quadratic equation will give us the value of 'w', which represents the width of the path.
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