The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle?
Let's assume that the width of the rectangular field is "x" meters.
According to the given information, the length of the rectangular field is 18 meters longer than the width, so it is (x + 18) meters.
To calculate the total amount of fencing required, we need to consider that the field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides.
For the first part of the field:
- The length is (x + 18) meters.
- The width is x meters.
For the second part of the field:
- The length is (x + 18) meters.
- The width is x meters.
We know that to calculate the amount of fencing required, we need to add up all the sides:
2 * length1 + 2 * width1 + 2 * length2 + 2 * width2 = 216 meters.
Substituting the values with the given information:
2 * (x + 18) + 2 * x + 2 * (x + 18) + 2 * x = 216.
Simplifying the equation further:
2x + 36 + 2x + 2x + 36 + 2x = 216,
8x + 72 = 216,
8x = 216 - 72,
8x = 144,
x = 144 / 8,
x = 18.
So, the width of the rectangular field is 18 meters.
Now, we can find the length:
Length = x + 18 = 18 + 18 = 36 meters.
Therefore, the dimensions of the outside rectangle are 36 meters in length and 18 meters in width.
To solve this problem, we can set up a system of equations based on the given information.
Let's denote the width of the rectangular field as "w" meters.
According to the problem, the length of the field is 18 meters longer than the width, so we can express it as "w + 18" meters.
Now, we can calculate the perimeter of the outside rectangle by adding up all the sides.
Perimeter = 2(length + width)
In this case, the length and width are "w + 18" and "w" meters, respectively.
So, the equation becomes:
216 = 2(w + 18 + w)
Now we can solve the equation to find the value of w.
216 = 2(2w + 18)
216 = 4w + 36
4w = 216 - 36
4w = 180
w = 180/4
w = 45
Now that we have found the value of w, we can substitute it back into the equation to find the length.
Length = w + 18
Length = 45 + 18
Length = 63
Therefore, the width of the rectangular field is 45 meters and the length is 63 meters.
From your description, I am not sure that the fencing is around the whole perimeter of the field. If it is:
L = W + 18
2L + 2W = 216
2(W + 18) + 2W = 216
Solve for W, then put value in the first equation to solve for L. Check by inserting both values into the second equation.