Given;
Preimeter of QRST = Perimeter of LMNP
Perimeter of LMNP = 17x
So,
Perimeter of QRST LMNP = 17x
Now,
Length of QRST = 2x + 9
Width = ?
We know,
Perimeter = 2 (l + w)
17 x = 2 (2 x + 9 + w)
17 x = 4 x + 18 + 2 w
17 x -4 x - 18 = 2 w
13 x - 18 = 2 w
w = (13 x - 18) / 2
<-- our answer
Preimeter of QRST = Perimeter of LMNP
Perimeter of LMNP = 17x
So,
Perimeter of QRST LMNP = 17x
Now,
Length of QRST = 2x + 9
Width = ?
We know,
Perimeter = 2 (l + w)
17 x = 2 (2 x + 9 + w)
17 x = 4 x + 18 + 2 w
17 x -4 x - 18 = 2 w
13 x - 18 = 2 w
w = (13 x - 18) / 2