Let's analyze the given figure. Since we are given a triangle with a line that is parallel to one of its sides, we can use the Triangle Proportionality Theorem.
The lengths of the segments intercepted by the parallel line are proportional. Let's write a proportion using the expressions for the lengths of the segments.
AB/BC=AE/ED
Since we are given the lengths of BC and AC, we can find length of AB.
As we know the length of AD, but not AE or ED, we can write AE=AD-ED. Now we can substitute all known lengths into our proportion.
AB/BC=AE/ED
⇕
6/8=21-ED/ED
Finally, we will solve this equation for ED.
