A resident of a building displays a Christmas tree-shaped light decoration on the building's exterior wall, as shown in the figure. From a certain point $P$ on the fifth floor exterior wall, small light bulbs are pulled to the two ends $A , B$ of the fourth floor to form an isosceles triangle $P A B$, where $\overline { P A } = \overline { P B }$; light bulbs are pulled to the two ends $C , D$ of the third floor to form an isosceles triangle $P C D$; light bulbs are pulled to the two ends $E , F$ of the second floor to form an isosceles triangle $PEF$. Assume each floor has equal height and each floor has equal length. If the length of the line segment cut out by the fifth floor inside triangle $P A B$ is $\frac { 1 } { 3 }$ of the floor length, what fraction of the floor length is the length of the line segment cut out by the fifth floor inside triangle $PEF$? (Light decoration thickness is negligible)
(1) $\frac { 1 } { 7 }$
(2) $\frac { 1 } { 6 }$
(3) $\frac { 1 } { 5 }$
(4) $\frac { 2 } { 9 }$
(5) $\frac { 1 } { 4 }$