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HELP For what values of x is the perimeter of the figure greater than 112 ​meters?

HELP For what values of x is the perimeter of the figure greater than 112 ​meters-example-1

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HELP For what values of x is the perimeter of the figure greater than 112 ​meters-example-1
User Meadow
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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.

User Robert Horvick
by
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