A rectangular lawn measures 14m by 8m. It is sorrounded by a path of uniform width. If the area of path is 48m^, find its width
length = 14 + 2w
width = 8 + 2w
so
48 = (14+2w) (8+2w) - 14*8
48 = 44 w + 4 w^2
w^2 + 11 w - 12 = 0
(w+12)(w-1) =0
w = 1
NOW CHECK
16*10 - 14*8 = 160 - 112 = 48, CARAMBA !!1!
Mwasya
Well, if you're looking for the width of the path, I guess you could say it's in "meters wide" territory. But let's do a little math to find it.
The total area of the rectangular lawn and the path combined is the sum of their individual areas. Since the area of the path is 48 square meters, we can subtract that from the total area to find the area of just the lawn.
The total area of the rectangle is found by multiplying its length (14m) by its width (8m): 14m * 8m = 112 square meters.
So now we know that the area of the lawn is 112 square meters, and the area of the path is 48 square meters. To find the width of the path, we need to subtract the area of the lawn from the total area: 112m^2 - 48m^2 = 64m^2.
The path forms a rectangular shape around the lawn, and the width is the same on all sides. So, we can divide the area of the path by its length to find the width: 64m^2 / 14m = 4.57m.
So, the width of the path is approximately 4.57 meters.
To find the width of the path surrounding the rectangular lawn, we can use the formula for the area of a rectangle:
Area = Length × Width
Given:
Length of the rectangular lawn = 14m
Width of the rectangular lawn = 8m
We can calculate the total area of the rectangular lawn, including the path, using the given information:
Total Area = (Length + 2 × Width of the path) × (Width + 2 × Width of the path)
The area of the path itself is given as 48m^2, so we know that:
Area of the path = Total Area - Area of the lawn
Now, we can substitute the given values into the formulas and solve for the width of the path:
Area of the lawn = Length × Width
Area of the lawn = 14m × 8m
Area of the lawn = 112m^2
Total Area = (14m + 2 × Width of the path) × (8m + 2 × Width of the path)
Area of the path = Total Area - Area of the lawn
48m^2 = (14m + 2 × Width of the path) × (8m + 2 × Width of the path) - 112m^2
Now, we can rearrange the equation and solve for the width of the path.
To find the width of the path surrounding the rectangular lawn, we can start by finding the total area of the entire layout (the combined area of the lawn and the path).
We know that the length of the rectangular lawn is 14m, and the width is 8m.
The area of the rectangular lawn can be calculated by multiplying the length and width: 14m * 8m = 112m².
Next, we need to find the total area of the layout by adding the area of the rectangular lawn and the area of the path. We are given that the area of the path is 48m².
So, the total area of the layout is 112m² + 48m² = 160m².
Now, let's assume that the width of the path surrounding the lawn is 'x'.
Since the path surrounds the entire lawn, the overall dimensions of the layout would be increased by 2x (x on each side).
Therefore, the length of the entire layout would be (14m + 2x) and the width would be (8m + 2x).
The area of the entire layout can be calculated by multiplying the length and width: (14m + 2x) * (8m + 2x) = 160m².
Expanding this equation, we get:
112m² + 28m²x + 16mx + 4x² = 160m².
Now, we can rearrange the equation and simplify it:
4x² + 16mx + 28m²x = 160m² - 112m²,
4x² + 16mx + 28m²x = 48m².
Dividing the entire equation by 4 to simplify it further:
x² + 4mx + 7m²x = 12m².
Now, we have a quadratic equation in terms of 'x'. To solve for 'x', we need to bring all the terms to one side and set the equation equal to zero:
x² + 4mx + 7m²x - 12m² = 0.
From here, we can use factoring, quadratic formula, or any other suitable technique to find the values of 'x'.
Once we find the roots of the equation, we will have the possible values for the width of the path surrounding the lawn.