The perimeter of a rectangle is 68 ft. the ratio of the length to the width is 9 : 8. what are the dimensions of the rectangle?

Perimeter of a rectangle=2(length)+2(width)
length=x
width=y

We can suggest the following system of equations:
2x+2y=68
x/y=9/8

We solve this system of equations by substitution method.
2x+2y=68  ⇒x+y=34  ⇒y=34-x

x/(34-x)=9/8
8x=9(34-x)
8x=306-9x
8x+9x=306
17x=306
x=306/17
x=18

y=34-x
y=34-18
y=16

dimensions of a rectanctle=length x width
dimensions of a rectangle=18  x 16

the dimensions of this rectangle will be 18 x 16  (ft)

The answer would be 7 cages