Answer:
The length of [tex]\overline{AD}[/tex] is 20 inches
Step-by-step explanation:
The given parameters are;
Triangle ABC is similar to triangle DEC, therefore, we can write, ΔABC~ΔDEC
[tex]\overline{AC}[/tex] = 30 inches
[tex]\overline{BA}[/tex] = 18 inches
[tex]\overline{ED}[/tex] = 6 inches
By similar triangles formula, we have;
[tex]\overline{BA}[/tex]/[tex]\overline{ED}[/tex] = [tex]\overline{AC}[/tex]/[tex]\overline{DC}[/tex]
Substituting the known values gives;
18/6 = 30/[tex]\overline{DC}[/tex]
Therefore, [tex]\overline{DC}[/tex] = 30/(18/6) = 30/18 × 6 = 10
[tex]\overline{DC}[/tex] = 10
[tex]\overline{AD}[/tex] = [tex]\overline{AC}[/tex] - [tex]\overline{DC}[/tex] = 30 - 10 = 20
[tex]\overline{AD}[/tex] = 20 inches.
