First, we will find the value of x
Using P = 21 + 2w
l= (x+ 4) and w =(2x - 7) P=42
substituting the above into the equation
42 = 2(x+4) + 2(2x-7)
open the parenthesis
42 = 2x +8 + 4x - 14
42 = 6x - 6
add 6 to both-side of the equation
42 + 6 = 6x -6 + 6
48 = 6x
divide both-side of the equation by 6
48/6 = 6x/6
8 = x
x=8
The length of the rectangle = x + 4 = 8 + 4 = 12cm
The width of the reactangle = 2x - 7 = 2(8) - 7 = 16-7 =9cm
The dimensions are 12cm by 9cm