The perimeter of the shape is greater than 112 meters for all values of x greater than 27. and the correct option is D.
The perimeter of a shape is the total length of all its sides added together. In this case, the shape has four sides, each of which has a different length. The lengths of the sides are x+2, x, x, and x+2. Therefore, the perimeter of the shape is:
Perimeter = (x+2) + x + x + (x+2)
Simplifying the expression, we get:
Perimeter = 4x + 4
We are given that the perimeter of the shape is greater than 112 meters. This means that the following inequality is true:
Perimeter > 112
Substituting the expression for the perimeter into the inequality, we get:
4x + 4 > 112
Subtracting 4 from both sides gives:
4x > 108
Dividing both sides by 4 gives:
x > 27
Therefore, the perimeter of the shape is greater than 112 meters for all values of x greater than 27. In other words, the answer is x>27.
Here is a table of values to illustrate the solution:
| x | Perimeter |
| 25 | 104 |
| 26 | 108 |
| 27 | 112 |
| 28 | 116 |
| 29 | 120 |
As you can see, the perimeter of the shape only becomes greater than 112 meters when x is greater than 27.