A Plot of land was 20m by 18 m.After a uniform path was made all round the plot , the area of the plot became 224m.How wide was the path?
width of path --- x m
original area = 20(18) = 360
after path added,
width --- 18+2x
length ---- 20 + 2x
new area of whole thing = (18+2x)(20+2x)
that is supposed be 224 m, which makes no sense at all,
first of all it should be m^2, secondly how can the area get smaller
after adding the path ???
check your post
The path was cut from the original plot , hence reduced the size of the plot.
That is not what the original question said, but ...
ok, then we would have
new area
= (20-2x)(18-2x)
= 4x^2 - 76x + 360
= 225
4x^2 - 76x + 135 = 0
x = (76 ± √3616)/8 = appr 1.98 m or appr 17.02 m
reject the last answer, since it would yield negative widths and lengths.
the path is appr 2 m wide
To find the width of the path, we need to subtract the area of the original plot from the area of the plot after the path was made. Let's break down the problem into steps:
Step 1: Find the area of the original plot
The original plot of land is a rectangle measuring 20m by 18m. To find the area, we use the formula: Area = length × width.
Original Area = 20m × 18m = 360m²
Step 2: Find the area of the plot after the path was made
The total area of the plot with the path is given as 224m².
Step 3: Calculate the area of the path
Area of the path = Area after path - Original area
Area of the path = 224m² - 360m²
Area of the path = -136m²
From the calculation, we find that the area of the path is negative, which is not possible in this context. It means there has been a mistake or inconsistency in the provided information or calculations. Please double-check the numbers and ensure their accuracy.