Answer:
[tex]CE=25\ units[/tex]
Step-by-step explanation:
we know that
If AB is parallel to CD. then triangles CED and BEA are similar
If two figures are similar, the ratio of its areas is equal to the scale factor squared
Let
z------> the scale factor
x-----> the area of triangle CED
y-----> the area of triangle BEA
so
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]x=425\ units^{2}[/tex]
[tex]y=68\ units^{2}[/tex]
substitute and solve for z
[tex]z^{2}=\frac{425}{68}[/tex]
[tex]z^{2}=6.25[/tex]
[tex]z=2.5[/tex] ------> the scale factor
Remember that
If two figures are similar, the ratio of its corresponding sides is equal to the scale factor
so
[tex]z=\frac{CE}{BE}[/tex]
we have
[tex]z=2.5[/tex]
[tex]BE=10\ units[/tex]
substitute and solve for CE
[tex]2.5=\frac{CE}{10}[/tex]
[tex]CE=2.5*10=25\ units[/tex]
