A developer wants to build homes on a rectangular plot of land 4 kilometers long and 3 kilometers wide. In this part of the city, regulations require a greenbelt of uniform width along two adjacent sides. The greenbelt must be 10 times the area of the development. find the width of the greenbelt.
area of development = 3*4 = 12 km^2
greenbelt area = 120 km^2:
one end = (3+w) by w
other end = 4 by w
so
120 = 4 w + 3 w + w^2 = w^2 + 7 w
w^2 + 7 w - 120 = 0
w = [ -7 +/- sqrt (49+480) ] / 2
= [ -7 +/- 23]/2
use + root only
w = 8
Ah, the joys of building regulations! Let me put on my clown shoes and calculate this for you!
First, let's find the area of the development. The rectangular plot is 4 kilometers long and 3 kilometers wide, so the area of the development is 4 km * 3 km = 12 square kilometers.
According to the regulations, the greenbelt must be 10 times the area of the development. So, the area of the greenbelt is 10 * 12 square kilometers = 120 square kilometers.
Now, we need to find the width of the greenbelt. Let's call it 'x' kilometers.
To calculate the width, we need to find the difference in the lengths of the adjacent sides (because the greenbelt is only along two adjacent sides).
So, the difference in lengths is (4 km - x) kilometers, and the width of the greenbelt is x kilometers.
The area of the greenbelt is the product of the difference in lengths and the width, so we have:
(4 km - x) km * x km = 120 square kilometers.
Expanding that equation, we have:
4x - x^2 = 120.
Now, let's solve this quadratic equation. Rearranging it, we get:
x^2 - 4x + 120 = 0.
Unfortunately, this quadratic equation doesn't have real solutions. So, it seems we've hit a road bump! It looks like the width of the greenbelt cannot be determined given the regulations and the dimensions of the plot.
But hey, look on the bright side! At least we've had some fun with math and clowns along the way, right?
To find the width of the greenbelt, we first need to calculate the area of the rectangular plot of land.
Given:
Length of the land = 4 kilometers
Width of the land = 3 kilometers
The area of the rectangular plot of land is calculated by multiplying the length and the width:
Area of the land = Length × Width
Area of the land = 4 km × 3 km
Area of the land = 12 km²
Next, we need to find the area of the greenbelt, which is required to be 10 times the area of the development.
Area of the greenbelt = 10 × Area of the land
Area of the greenbelt = 10 × 12 km²
Area of the greenbelt = 120 km²
To find the width of the greenbelt, we divide the area by the length of the land. Since the greenbelt extends along two adjacent sides, we divide the area by 2 times the length of the land.
Width of the greenbelt = Area of the greenbelt / (2 × Length of the land)
Width of the greenbelt = 120 km² / (2 × 4 km)
Width of the greenbelt = 120 km² / 8 km
Width of the greenbelt = 15 km
Therefore, the width of the greenbelt is 15 kilometers.
To find the width of the greenbelt, we first need to calculate the area of the rectangular plot of land.
The area of a rectangle is calculated by multiplying its length by its width. In this case, the length is given as 4 kilometers, and the width is given as 3 kilometers. Therefore, the area of the plot of land is:
Area = Length x Width
Area = 4 km x 3 km
Area = 12 square kilometers
Next, we need to find the area of the greenbelt, which is required to be 10 times the area of the development.
Area of Greenbelt = 10 x Area of Development
Area of Greenbelt = 10 x 12 square kilometers
Area of Greenbelt = 120 square kilometers
Now that we have the area of the greenbelt, we can calculate its width. Since the greenbelt has uniform width along two adjacent sides, we can assume it as a rectangular strip.
The formula to calculate the area of a rectangle is:
Area = Length x Width
In this case, we know the area of the greenbelt, which is 120 square kilometers, and we need to find its width. Let's assume the width of the greenbelt as "w" kilometers. Since we know the area and length, we can write the equation as:
120 km^2 = 4 km x w km
Now, let's solve the equation for "w" by dividing both sides by 4 km:
w km = (120 km^2) / (4 km)
w km = 30 km
Therefore, the width of the greenbelt is 30 kilometers.