Answer:
[tex]LE=2.5\ units[/tex]
Step-by-step explanation:
In this problem we assume that
Segment PL, Segment AE and Segment RT are parallels
so
using proportion
[tex]\frac{PA}{PR}=\frac{LE}{LT}[/tex]
we have
[tex]PA=7\ units\\ PR=21\ units\\ ET=5\ units[/tex]
Remember that
[tex]LT=LE+ET=LE+5[/tex]
substitute the values and solve for LE
[tex]\frac{7}{21}=\frac{LE}{LE+5}[/tex]
Multiply in cross
[tex]7(LE+5)=21(LE)[/tex]
[tex]7LE+35=21LE[/tex]
[tex]21LE-7LE=35[/tex]
[tex]14LE=35[/tex]
[tex]LE=2.5\ units[/tex]
