a farmer wishes to enclose a rectangular region with 210 meters of fencing in such a way that the length is twice the width and the region is divided into two equal parts. what length and width should be used?
Width = X-meters.
Length = 2X-metes.
Divider = 2X-meters.
2*x + 2*2x + 2x = 210m,
2x + 4x + 2x = 210,
8x = 210,
X = 26.25m. = Width.
2X = 2*26.25 = 52.5m. = Length.
2X = 52.5 = Divider.
26.25 is the width and the length is 52.25
x=width(since the width has three sections, left side, middle and right side, it becomes 3x)
2x=length
so equation is:
2*2x(upper and lower lengths)+3x(left side, middle and right side)=210
2*2x+3x=210
4x+3x=210
7x=210
x=30
2x=60
so the length is 60m and the width is 30m.
To find the length and width of the rectangular region, we can set up an equation and solve for the variables.
Let's assume the width of the rectangular region is "w" meters. According to the given conditions, the length is twice the width, so the length will be "2w" meters.
To find the perimeter of the rectangle, we add up all the sides:
Perimeter = 2(Length) + 2(Width)
Since we are given that the perimeter is 210 meters, we can set up the equation:
210 = 2(2w) + 2(w)
Simplifying the equation, we have:
210 = 4w + 2w
Combining like terms, we get:
210 = 6w
Now divide both sides by 6 to solve for the value of "w":
w = 210 / 6
w ≈ 35
Therefore, the width of the rectangular region is approximately 35 meters.
Now, using this value, we can find the length:
Length = 2w = 2(35) = 70 meters
So, for the farmer to enclose a rectangular region with 210 meters of fencing, with the length being twice the width and the region divided into two equal parts, the width used should be 35 meters and the length should be 70 meters.