Question

The rectangle below has a length of 3x2+7x-5and a width of -x2-4x+2. Find the perimeter of the rectangle and explain how you arrived at your solution.

Answer 1

P = 4x² +6x -6

Explanation:

We will use the formula for perimeter in terms of side lengths, then fill in the values given for the side lengths and simplify the result.

The perimeter (P) of a rectangle is given by the formula ...

P = 2(L +W)

where L and W represent the length and width. Filling in your given information, we have ...

P = 2((3x² +7x -5) +(-x² -4x +2))j

Collecting terms inside parentheses gives ...

P = 2((3-1)x² +(7-4)x +(-5+2)) = 2(2x² +3x -3)

Using the distributive property gives ...

P = 4x² +6x -6