Answer:
[tex]\boxed{4x-8}[/tex]
Step-by-step explanation:
Rectangle A
The length of this rectyangle is: [tex]l=2x+8[/tex]
The width of this rectangle is: [tex]w=x-1[/tex]
Perimeter of rectangle A
The perimeter is given by:
[tex]P=2l+2w[/tex]
We substitute the expressions and simplify:
[tex]P=2(2x+8)+2(x-1)[/tex]
[tex]P=4x+16+2x-2[/tex]
[tex]P=4x+2x+16-2[/tex]
[tex]P=6x+14[/tex]
Rectangle B.
The length of this rectangle is: [tex]3x+5[/tex]
The width of this rectangle is :[tex]w=2x-2[/tex]
Perimeter of rectangle B
We apply the formula for perimeter again to obtain;
[tex]P=2(3x+5)+2(2x-2)[/tex]
[tex]\Rightarrow P=6x+10+4x-4[/tex]
[tex]\Rightarrow P=6x+4x+10-4[/tex]
[tex]\Rightarrow P=10x+6[/tex]
Perimeter of rectangle B minus perimeter of rectangle A
[tex](10x+6)-(6x+14)[/tex]
[tex]=10x+6-6x-14[/tex]
[tex]=10x-6x+6-14[/tex]
[tex]=4x-8[/tex]
