The dimensions of a rectangular plot of ground is 12m by 10m. A rectangular pool is dug at the centre of the plot surrounded by a path of uniform width. If the area of the pool is 2/3 of the area of the plot, find the width of the path
The dimensions of a rectangular plot of ground is 12m by 10m. A rectangular pool is dug at the centre of the plot surrounded by a path of uniform width. If the area of the pool is 2/3 of the area of the plot, find the width of the path
To find the width of the path surrounding the rectangular pool, we can start by calculating the area of the rectangular plot and the area of the pool.
Given:
Dimensions of the rectangular plot: 12m by 10m
Step 1: Calculate the area of the rectangular plot
Area of the plot = length × width
Area of the plot = 12m × 10m = 120m²
Step 2: Calculate the area of the pool
Let's assume the width of the path surrounding the pool is denoted by "x."
The dimensions of the pool will be smaller than the plot by twice the width of the path.
Length of the pool = 12m - 2x
Width of the pool = 10m - 2x
Area of the pool = (length of pool) × (width of pool)
Area of the pool = (12m - 2x) × (10m - 2x)
Given that the area of the pool is 2/3 of the area of the plot, we can set up the equation:
(12m - 2x) × (10m - 2x) = (2/3) × 120m²
Step 3: Solve the equation for x
Expand the equation and simplify:
(120m - 24xm - 20xm + 4x²) = (2/3) × 120m²
120m - 44xm + 4x² = (2/3) × 120m²
Multiply both sides by 3 to remove the fraction:
360m - 132xm + 12x² = 240m²
Rearrange the equation to get it in the standard form of a quadratic equation:
12x² - 132xm + (240m² - 360m) = 0
Simplify further:
12x² - 132xm + 120m(2m - 3) = 0
Now, we can solve this quadratic equation for x using factoring, completing the square, or the quadratic formula. However, it seems that there might be an error in the problem statement or calculation because there is a missing value for the length "m" in the given information.
Please double-check the given dimensions or provide any missing information so that I can assist you further in finding the width of the path surrounding the pool.
0 Response to "The dimensions of a rectangular plot of ground is 12m by 10m. A rectangular pool is dug at the centre of the plot surrounded by a path of uniform width. If the area of the pool is 2/3 of the area of the plot, find the width of the path"
Post a Comment