(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
Accepted Solution
A:
Answer:[tex]\boxed{4x-8}[/tex]Step-by-step explanation:Rectangle AThe length of this rectyangle is: [tex]l=2x+8[/tex]The width of this rectangle is: [tex]w=x-1[/tex]Perimeter of rectangle AThe 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 BWe 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]