Answer:
[tex]AE=\frac{50}{3}\ units[/tex]
Step-by-step explanation:
step 1
In the right triangle ABC
Applying the Pythagoras Theorem fin the hypotenuse AC
[tex]AC^{2} =AB^{2}+BC^{2}[/tex]
substitute
[tex]AC^{2} =6^{2}+8^{2}[/tex]
[tex]AC^{2} =100[/tex]
[tex]AC =10\ units[/tex]
step 2
we know that
If two figures are similar, then the ratio of its corresponding sides is equal
so
[tex]\frac{AB}{CD}=\frac{AC}{CE}[/tex]
substitute and solve for CE
[tex]\frac{6}{4}=\frac{10}{CE}\\ \\CE=4*10/6\\ \\CE=\frac{20}{3}\ units[/tex]
step 3
Find the length of segment AE
AE=AC+CE
substitute the values
[tex]AE=10\ units+\frac{20}{3}\ units=\frac{50}{3}\ units[/tex]
