a path #m wide surround a rectangular garden 15M wide and 18m long .what is the area of the path?
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Add twice the width, w, of the path to the length, all it Length = 18+2w
Add twice the width of the path to the width, call it Breadth = 15+2w
calculate the area of the big rectangle (18+2w)(15+2w)
subtract the inside rectangle
(18+2w)(15+2w) - 18*15
= 66w+4w^2
Thanks
To find the area of the path, we need to subtract the area of the rectangular garden from the area of the larger rectangle formed by the path.
1. Calculate the area of the rectangular garden:
Area of rectangular garden = length × width
Area of rectangular garden = 15m × 18m
Area of rectangular garden = 270 square meters
2. Calculate the dimensions of the larger rectangle:
The garden is surrounded by a path on all four sides, which means the length and width of the larger rectangle will be increased by twice the width of the path.
Length of larger rectangle = 18m + 2 × (m width of the path)
Width of larger rectangle = 15m + 2 × (m width of the path)
3. Calculate the area of the larger rectangle:
Area of larger rectangle = (length of larger rectangle) × (width of larger rectangle)
Area of larger rectangle = (18m + 2 × m) × (15m + 2 × m)
4. Subtract the area of the rectangular garden from the area of the larger rectangle to find the area of the path:
Area of the path = Area of larger rectangle - Area of rectangular garden
Example with a path width of 3m:
Area of larger rectangle = (18m + 2 × 3m) × (15m + 2 × 3m) = 24m × 21m = 504 square meters
Area of the path = 504 square meters - 270 square meters = 234 square meters
Therefore, the area of the path is 234 square meters.