Sidewalk of uniform width has area of 180 ft squared and is surrounded ny a flower bed that 11 ft wide and 13 ft long. Find the width of the sidewalk?
By my calculations, the sidewalk could be an incredible 12 feet long and 15 feet wide.
To find the width of the sidewalk, we need to subtract the area of the flower bed from the total area of the sidewalk and flower bed combined.
First, let's find the area of the flower bed:
Area of flower bed = Length × Width = 13 ft × 11 ft = 143 ft²
Next, we subtract the area of the flower bed from the total area to get the area of just the sidewalk:
Area of sidewalk = Total area - Area of flower bed = 180 ft² - 143 ft² = 37 ft²
Since the sidewalk has a uniform width, we can assume that the width of the sidewalk is the same on all sides. To find the width of the sidewalk, we need to find the length of one side, as the width will be the same on both sides.
Since the sidewalk is rectangular in shape, we can use the formula for the area of a rectangle to find the length of one side:
Area of sidewalk = Length × Width
Plugging in the values we have:
37 ft² = Length × Width
We know that the length of one side of the sidewalk is equal to the width, so we can rewrite the formula:
37 ft² = Width²
To find the width, we need to take the square root of both sides:
√(37 ft²) = √(Width²)
Simplifying:
√37 ft = Width
Therefore, the width of the sidewalk is approximately 6.08 ft.