Question

(07.02) The following table shows the length and width of two rectangles: Length Width Rectangle A 2x + 8 x − 1 Rectangle B 3x + 5 2x − 2 Which expression is the result of the perimeter of rectangle B minus the perimeter of rectangle A? (1 point) 16x + 20 2x − 4 4x − 8 8x + 10

Answer 1

4x - eight

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Answer 2

`\boxed{4x-8}`

Explanation:

Rectangle A

The length of this rectyangle is:
`l=2x+8`

The width of this rectangle is:
`w=x-1`

Perimeter of rectangle A

The perimeter is given by:

`P=2l+2w`

We substitute the expressions and simplify:

`P=2(2x+8)+2(x-1)`

`P=4x+16+2x-2`

`P=4x+2x+16-2`

`P=6x+14`

Rectangle B.

The length of this rectangle is:
`3x+5`

The width of this rectangle is :
`w=2x-2`

Perimeter of rectangle B

We apply the formula for perimeter again to obtain;

`P=2(3x+5)+2(2x-2)`

`\Rightarrow P=6x+10+4x-4`

`\Rightarrow P=6x+4x+10-4`

`\Rightarrow P=10x+6`

Perimeter of rectangle B minus perimeter of rectangle A

`(10x+6)-(6x+14)`

`=10x+6-6x-14`

`=10x-6x+6-14`

`=4x-8`