Question

What is the simplified expression that represents the perimeter of the garden? A 14n B 14n−1 C 14n+7 D 14n+8

Answer 1

The simplified expression that represents the perimeter of the garden is D)
`\(14n + 8\).`

Step-by-step explanation:

To find the perimeter of the garden, we need to add the lengths of all its sides. In this case, the given answer choices are in the form
`\(14n + \text{{constant}}\)`. This suggests that the perimeter is a multiple of 14 with a constant term. By examining the options, we can determine that the correct expression is D)
`\(14n + 8\)`.

Consider the scenario where
`\(n = 0\)`, meaning there is no multiplication by
`\(n\)` in the expression. In this case, the perimeter is solely represented by the constant term. If
`\(n\)` were any other value, it would contribute to the perimeter by being multiplied by 14. This aligns with the
`\(14n\)` term in the expression. The constant term
`\(+8\)` signifies that even when
`\(n = 0\)`, there is a constant length contributing to the perimeter, making
`\(14n + 8\)` the appropriate simplified expression for the garden's perimeter.

In summary, the expression
`\(14n + 8\)` correctly represents the perimeter of the garden, accounting for the 14 units contributed by each
`\(n\)` and the constant
`\(+8\)` units, which is present even when
`\(n\)` is zero.