Perimeter of the rectangle = 34 cm
Let us assume the length of the rectangle = x
Let us assume the width of the rectangle = y
Then
Width of the rectangle can be determined by the equation
2x/3 = 3y/4
2x * 4= 3y * 3
8x = 9y
x = (9y)/8
Now
Perimeter of the rectangle = 2(length + width)
34 = 2(x + y)
34/2 = x + y
x + y = 17
Now let us put the value of x in terms of y in the second equation
x + y = 17
(9y/8) + y = 17
(9y + 8y)/8 = 17
17y = 17 * 8
y = (17 * 8)/17
= 8 cm
Now let us put the value of y in the equation
x + y = 17
x + 8 = 17
x = 17 - 8
= 9 cm
So the length of the rectangle is 9 cm and the width of the rectangle is 8 cm.