Question

The following table shows the length and width of two rectangles:

Length Width
Rectangle A 3x + 2 2x - 1
Rectangle B x + 5 5x - 1


Which expression is the result of the perimeter of rectangle B minus the perimeter of rectangle A?
2x + 2
2x + 6
22x + 14
22x + 18

Answer 1

2x+6

Explanation:

took the test

Answer 2

The perimeter of a rectangle is equal to two times the sum of the length and the width.

`P=2(l+w)`

Rectangle A:

`l=3x+2 \\ w=2x-1 \\ \\ P_A=2(3x+2+2x-1)=2(5x+1)=10x+2`

Rectangle B:

`l=x+5 \\ w=5x-1 \\ \\ P_B=2(x+5+5x-1)=2(6x+4)=12x+8`

The perimeter of rectangle B minus the perimeter of rectangle A:

`P_B - P_A=12x+8-(10x+2)=12x+8-10x-2=\boxed{2x+6}`