Let
rA--------> radius of the circle A
rB-------> radius of the circle B
LA------> the length of the intercepted arc for circle A
LB------> the length of the intercepted arc for circle B
we have that
rA=5/2 ft
rB=9/2 ft
rA/rB=5/9--------> rB/rA=9/5
LA=(25/24)π ft
we know that
if Both circle A and circle B have a central angle , the ratio of the radius of circle A to the radius of circle B is equals to the ratio of the length of circle A to the length of circle B
rA/rB=LA/LB--------> LB=LA*rB/rA-----> [(25/24)π*9/5]----> 15/8π ft
the answer is
the length of the intercepted arc for circle B is 15/8π ft