Hi!
I have been stuck on this problem for the past 20 minutes. Please help!
A rectangular garden 30m by 40m has two paths of equal width crossing through as shwon. Find the width of each path if the total area covered by the paths s 325m^2.
() - represents garden
t - represents how paths cross
( t ) - the paths are like a lower case t. One goes straight p and down and the second goes across.
They are 5 meters wide a piece which would give you 350 m^2. You then take away 25 meters for where they cross.
To find the width of each path, we first need to compute the area of the garden without the paths.
The total area of the rectangular garden is given by the formula:
Area = length * width
Given that the length of the garden is 30m and the width is 40m, we can calculate the area as follows:
Area = 30m * 40m = 1200m²
Next, we need to subtract the area covered by the paths to obtain the remaining area of the garden.
Since there are two paths of equal width, let's denote the width of each path as 'w'.
The total area covered by the paths is given as 325m², so we can set up the equation:
325m² = 30m * w + 40m * w
Simplifying the equation, we have:
325m² = 70m * w
Now, we can solve this equation for 'w' by dividing both sides by 70m:
w = 325m² / 70m
Evaluating this, we have:
w ≈ 4.64m
Therefore, the width of each path is approximately 4.64 meters.
To find the width of each path, we can start by calculating the total area of the garden. The total area of the garden is given by the length multiplied by the width, which in this case is 30m x 40m = 1200m^2.
Since the two paths have equal width and form a lowercase "t" shape, the area of the paths can be considered as two rectangles. Let's denote the width of each path as 'w'. The area of the two rectangles representing the paths is then 2 * w * w = 2w^2.
According to the problem, the total area covered by the paths is given as 325m^2. So, we can set up the equation:
Total area of the garden - Area of the paths = 325m^2
1200m^2 - 2w^2 = 325m^2
Now, let's solve this equation to find the value of 'w'.
1200m^2 - 2w^2 = 325m^2
Rearranging the equation, we get:
2w^2 = 1200m^2 - 325m^2
2w^2 = 875m^2
Dividing by 2, we have:
w^2 = 875m^2 / 2
w^2 = 437.5m^2
To find the width 'w', we can take the square root of both sides:
w = √437.5m^2
w ≈ 20.9m
So, the width of each path is approximately 20.9 meters.