a rectangular plot of ground having dimensions 46 feet by 30 feet is surrounded by a walk of uniform width. If the area of the walk is 240 ftˆ2, what is its width?
area w/o walk: 46*30 = 1380
area w/walk (46+2w)(30+2w)
So, we have
(46+2w)(30+2w) - 1380 = 240
4w^2 + 152w + 1380 - 1380 = 240
4w^2 + 152w - 240 = 0
w^2 + 38w - 60 = 0
w = -19 + sqrt(421) = 1.5
Well, it seems we have quite a walking dilemma here! Let's calculate the width of that walkway, shall we?
First, we need to find the total area of both the rectangular plot and the walkway. The area of the rectangular plot is given by length multiplied by width, which is 46 feet multiplied by 30 feet, resulting in an area of 1380 square feet.
Now, we need to subtract the area of the rectangular plot from the total area (including the walkway) to find the area of just the walkway. So, if the area of the walkway is 240 square feet, we can subtract 240 from 1380, giving us 1140 square feet.
Since the walkway surrounds the entire rectangular plot, it has the same length as the rectangular plot (46 feet), and we need to find the width.
To find the width of the walkway, we divide the area of the walkway by the length of the rectangular plot. Therefore, the width of the walkway would be 1140 square feet divided by 46 feet, which is approximately 24.78 feet.
So, the width of the walkway is approximately 24.78 feet. Now, watch out for pedestrians and enjoy your nicely surrounded plot of ground!
To find the width of the walk, we first need to determine the dimensions of the inner rectangular plot, which is the area of the walk subtracted from the total area of the larger rectangle.
Given:
Length of the larger rectangle = 46 feet
Width of the larger rectangle = 30 feet
Area of the walk = 240 ft^2
To find the area of the larger rectangle, we use the formula:
Area = Length × Width
Area of the larger rectangle = 46 feet × 30 feet = 1380 ft^2
Now, to find the dimensions of the inner rectangle (the plot without the walk), we subtract the area of the walk from the area of the larger rectangle.
Area of the inner rectangle = Area of the larger rectangle - Area of the walk
Area of the inner rectangle = 1380 ft^2 - 240 ft^2
Area of the inner rectangle = 1140 ft^2
Since we know the dimensions of the inner rectangle, we can calculate its width and length.
Let's assume the width of the walk is "x" feet.
Length of the inner rectangle = Length of the larger rectangle minus twice the width of the walk.
Length of the inner rectangle = 46 feet - 2x
Width of the inner rectangle = Width of the larger rectangle minus twice the width of the walk.
Width of the inner rectangle = 30 feet - 2x
The area of the inner rectangle is given as 1140 ft^2, so we can set up an equation:
Area of the inner rectangle = Length of the inner rectangle × Width of the inner rectangle
1140 ft^2 = (46 feet - 2x) × (30 feet - 2x)
Now, we can solve this equation to find the value of "x", which is the width of the walk.