Question

If lines l, m, and n are parallel, and AB = 2, AC = 8, and EF = 5, what is the length of DE?

Answer 1

Consider the theorem that when a pair of transversals intersect more than two parallel lines, then the ratio of the corresponding segments are always equal.

According to the given problem,

$\begin{gathered} AB=2 \\ AC=8 \\ EF=5 \end{gathered}$

In the given figure, lines ABC and DEF intersect the set of parallel lines 'l', 'm', and 'n'.

Applying the above theorem,

$\frac{AB}{AC}=\frac{DE}{DF}$

The expression can be resolved as,

$\frac{AB}{AC}=\frac{DE}{DE+EF}$

Substitute the values,

$\begin{gathered} \frac{2}{8}=\frac{DE}{DE+5} \\ \frac{1}{4}=\frac{DE}{DE+5} \end{gathered}$

Transpose the terms to simplify,

$\begin{gathered} DE+5=4\cdot DE \\ 4DE-DE=5 \\ 3DE=5 \\ DE=\frac{5}{3} \end{gathered}$

Thus, the value of the segment DE is 5/3 units.