Question

The sides of a quadrilateral are shown below. Express the perimeter in terms of x. A. 4x^2 + 12 B. 6x + 12 C. 4x^2 + 40 D. 3x + 6

Answer 1

The perimeter of the quadrilateral in terms of
`\(x\) is \(3x + 6\).`

Step-by-step explanation:

To determine the perimeter of the given quadrilateral, sum the lengths of its four sides:

1.
`\(2x\)`

2.
`\(x + 3\)`

3.
`\(4x - 1\)`

4.
`\(x + 4\)`

Adding these side lengths:

`\[2x + (x + 3) + (4x - 1) + (x + 4) = 8x + 6.\]`

To simplify further, factor out \(2\) from both terms:

`\[2(4x + 3).\]`

Express it in the desired format
`\(3x + 6\)` by factoring out
`\(1\)` from
`\(4x + 3\):`

`\[2(4x + 3) = 2 \cdot 1 \cdot (4x + 3) = 1 \cdot (4x + 3).\]`

Therefore, the final expression for the perimeter in terms of
`\(x\)` is
`\(3x + 6\),` and the correct option is D.