Final Answer:
Alice needs 4x + 52 feet of fencing in total.
Step-by-step explanation:
To find the total amount of fencing needed, we must first find the perimeter of the rectangle. The perimeter of a rectangle is found by adding the length and width together and multiplying by 2.
In this case, the longer dimension, or length, of the rectangle is 27 feet. We are given that the width of the rectangle is 13 feet. So, the perimeter can be found by multiplying 2 by the sum of 27 and 13, which is 40. This gives us a perimeter of 80 feet.
However, this only accounts for three sides of the rectangle. We must also include the fourth side, which is the fence that Alice will be building. This fence will be the same length as the longer dimension, which is 27 feet. So, we must add this length to the perimeter to get the total amount of fencing needed.
This can be represented with the expression 80 + 27, or in simplified form, 4x + 52. This means that Alice needs 4x + 52 feet of fencing in total, where x represents the length of the shorter dimension.
So, if the longer dimension is 27 feet, we can plug in this value for x and get 4(27) + 52, which simplifies to 80 feet. This confirms that our expression is correct.
In conclusion, to find the total amount of fencing needed, we must find the perimeter of the rectangle and add the length of the fourth side, which is the fence. This can be represented by the expression 4x + 52 feet. By plugging in the value for the longer dimension, we can confirm that Alice needs 80 feet of fencing in total.