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To find the perimeter of the path constructed outside the rectangular park, we need to consider the dimensions of both the park and the path.
The park is 42 meters long and 19 meters wide. The path is constructed outside the park, and its width is 7.5 meters.
To calculate the perimeter of the path, we need to find the total length of all four sides of the outer rectangle formed by the park and the path.
The length of the outer rectangle will be the sum of the length of the park and twice the width of the path, since the path is constructed on both sides of the park:
Length of outer rectangle = Length of park + 2 × Width of path
= 42 m + 2 × 7.5 m
= 42 m + 15 m
= 57 m
Similarly, the width of the outer rectangle will be the sum of the width of the park and twice the width of the path:
Width of outer rectangle = Width of park + 2 × Width of path
= 19 m + 2 × 7.5 m
= 19 m + 15 m
= 34 m
Now, we can calculate the perimeter of the path (outer rectangle) by adding the lengths of all four sides:
Perimeter of path = 2 × (Length + Width) of outer rectangle
= 2 × (57 m + 34 m)
= 2 × 91 m
= 182 m
Therefore, the perimeter of the path is 182 meters.