Question

Find the polynomial that represents the perimeter of a rectangle that has a length of `3x-2` and width of `x+4`?

Answer 1

`"perimeter "=8x+4`

Explanation:

`" the perimeter of a rectangle is "`

`• " perimeter "=2l+2w`

`"where l is the length and w the width"`

`"here "l=3x-2" and "w=x+4`

`rArr"perimeter "=2(3x-2)+2(x+4)larrcolor(blue)"distribute"`

`color(white)(rArr"perimeter ")=6x-4+2x+8larrcolor(blue)"collect like terms"`

`color(white)(rArr"perimeter ")=8x+4`

Answer 2

Perimeter`=8x+4`

Explanation:

Perimeter of a rectangle is given by the formula `2*"length"+2*"width"`.

Length`=(3x-2)`, width`=(x+4)`

`2(3x-2)+2(x+4)`

`rArr (6x-4)+(2x+8)`

collecting (grouping) like terms:

`rArr 6x+2x+8-4`

`rArr 8x+4`