A farmer wishes to enclose a rectangular region with 196 meters of fencing in such a way that the length is twice the width and that the region is divided along its length into two equal parts. What is the length and width in meters?
Did you make a sketch?
width = x
length = 2x
but you dividing the length in two, so all sides are x
Count the x's , we need 7x
7x = 196
x = 28
the large rectangle is 54m by 28m
I assumed that the dividing side is parallel to the width.
If your dividing line is parallel to the length, then I would
define the original width as 2x and the length as 4x (thus avoiding fractions)
Then I see 3(4x) + 4(x) = 196
16x = 196
x = 12.25
and the field was 24.5m by 49 m
To solve this problem, let's start by assigning variables to the length and width of the rectangular region.
Let's assume the width of the rectangular region is 'W' meters.
Since the length is twice the width, we can set the length as '2W' meters.
The perimeter of the rectangular region is given as 196 meters. The perimeter of a rectangle is calculated by adding the lengths of all four sides, which in this case is equal to the sum of the length and width values:
Perimeter = 2(Length + Width)
Plugging in the values we have:
196 = 2(2W + W)
Now we can solve the equation step by step:
196 = 2(3W) [Simplified inside parentheses]
196 = 6W [Distributed the 2 to both terms inside parentheses]
W = 196 / 6 [Divided both sides by 6]
W ≈ 32.67
So, the width of the rectangular region is approximately 32.67 meters.
To find the length, we can substitute this value back into the equation for length:
Length = 2W ≈ 2 * 32.67 ≈ 65.34
Therefore, the length of the rectangular region is approximately 65.34 meters and the width is approximately 32.67 meters.
To solve this problem, we need to set up and solve a system of equations based on the given information.
Let's assume that the width of the rectangular region is "w" meters. According to the problem, the length of the rectangular region is twice the width, so the length would be "2w" meters.
To determine the perimeter of the rectangle, we add up the lengths of all four sides. Since the perimeter is given as 196 meters, we can write the following equation:
Perimeter = 2w + 2(2w) = 196
Simplifying the equation, we get:
2w + 4w = 196
6w = 196
w = 196/6
w ≈ 32.67
So, the width of the rectangular region is approximately 32.67 meters.
Since the length is twice the width, the length would be:
2w ≈ 2(32.67) ≈ 65.34
Therefore, the length of the rectangular region is approximately 65.34 meters.
To recap, the length and width of the rectangular region are approximately 65.34 meters and 32.67 meters, respectively.