Aisha wants to build a fence for the goat exhibit. She has 14 meters of fencing. Draw two ways that Aisha could build the fence.
it could be a rectangle such that the length+width = 7 meters
It might be a circle with circumference = 14
or a triangle, or ...
use your imagination.
Gfg
There are two possible ways that Aisha could build the fence using 14 meters of fencing:
1. Square-shaped enclosure:
- If Aisha wants to create a square-shaped enclosure, she would need to use all 4 sides of the fencing equally.
- Each side would be 14 meters divided by 4, which is 3.5 meters.
- Therefore, Aisha could build a square-shaped fence with each side measuring 3.5 meters.
2. Rectangular-shaped enclosure:
- Another option for Aisha is to create a rectangular-shaped enclosure.
- In this case, she would need to allocate different lengths to the longer and shorter sides of the fence.
- For example, she could use 6 meters on one side, and 2 meters on the other side.
- This would leave her with a remaining 6 meters to use for the other two sides.
- Therefore, Aisha could build a rectangular-shaped fence with sides measuring: 6 meters, 2 meters, 6 meters, and 2 meters.
To draw two ways that Aisha could build the fence, we first need to determine the dimensions of each potential fence. Let's explore the possibilities:
Option 1: Rectangular Fence
To build a rectangular fence, we need to consider the length and width. Let's say Aisha wants to maximize the area of the enclosure:
- Length: Let's assign the variable "l" to represent the length of the fence.
- Width: Since it is a rectangular fence, the opposite sides (width) have the same length. Let's assign the variable "w" to represent the width of the fence.
The perimeter of a rectangle is given by the formula: P = 2l + 2w. In this case, the perimeter equals the available fencing, which is 14 meters. Thus, we have the equation: 2l + 2w = 14.
Now, let's determine the possible dimensions for the rectangular fence by assigning values to one variable and solving for the other. Here are two examples:
Example 1:
Let's assume the width (w) is 2 meters. By substituting this value into the equation, we get: 2l + 2(2) = 14 -> 2l + 4 = 14 -> 2l = 10 -> l = 5.
So, for this example, the dimensions of the rectangular fence are: length = 5 meters and width = 2 meters.
Example 2:
Assuming the width (w) is 3 meters, we can repeat the process: 2l + 2(3) = 14 -> 2l + 6 = 14 -> 2l = 8 -> l = 4.
Thus, for this example, the dimensions of the rectangular fence are: length = 4 meters and width = 3 meters.
Option 2: Square Fence
Another possibility is that Aisha builds a square fence, where all sides have equal lengths.
- Assign the variable "s" to represent the length of each side of the square fence.
The perimeter of a square is given by the formula: P = 4s. Again, the perimeter must be equal to the available fencing, which is 14 meters in this case. So we have the equation: 4s = 14.
Let's solve for the length of each side by dividing both sides of the equation by 4: s = 14/4 -> s = 3.5.
Therefore, for a square fence, each side should have a length of 3.5 meters.
Now that we have determined the dimensions for both a rectangular and a square fence, you can proceed to draw the two possible configurations based on these specifications.