Answer:
Lengths of AB and BD could be 4 and 2.
Step-by-step explanation:
By using Basic Proportionality Theorem - If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
\(\frac{AB}{BD}=\frac{AC}{CE}\)
so we can say, \(\frac{AB}{AD}=\frac{AC}{AE}=\frac{BC}{DE}\)
\(\frac{AB}{AD}=\frac{BC}{DE}\)
\(\frac{AB}{AD} =\frac{2}{3}\)
take resiprocal of both sides
\(\frac{AD}{AB} =\frac{3}{2}\)
subtract 1 form both sides
\(\frac{AD}{AB} - 1 = \frac{3}{2}-1\)
we get, \(\frac{AD-AB}{AB} =\frac{3-2}{2}\)
\(\frac{BD}{AB} =\frac{1}{2}\)
take resiprocal of both sides
\(\frac{AB}{BD} =\frac{2}{1} =\frac{4}{2}\)
Thus, lengths of AB and BD could be 4 and 2.
