Question

Find a polynomial that represents the perimeter of the rectangle.

Answer 1

`4x^2+12x+22`

Explanation:

The perimeter of a rectangle is equal to
`2l+2w` where l is the length and w is the width. So, this rectangle would be equal to
`2\left(x+3\right)+2\left(2x^2+5x+8\right)`. Then, to find the polynomial simplify the expression. To do this first distribute the two 2s. This equals
`2x+6+4x^2+10x+16`. Then, add like terms to finish simplifying. This gives you the final answer of
`4x^2+12x+22`.

Answer 2

Hi there!

`\large\boxed{P = 4x^2 + 12x + 22}`

The perimeter of a rectangle is:

P = 2l + 2w

Thus, plug in the given length and width:

P = 2(2x² + 5x + 8) + 2(x + 3)

Distribute:

P = 2(2x²) + 2(5x) + 2(8) + 2(x) + 2(3)

Simplify:

P = 4x² + 10x + 16 + 2x + 6

Combine like terms:

P = 4x² + 12x + 22