Answer:
12 miles
Explanation:
Two triangles are similar if their two corresponding angles are congruent (equal) to each other.
if their two corresponding angles are of equal this also means that the third angle is also equal and corresponding.
ΔABC ∼ ΔEDC (two corresponding angles are congruent)
Therefore to find the sides, we use the following proportions:
[tex]\frac{AC}{AE}=\frac{BC}{BD}=\frac{DE}{AB}[/tex]
BC = x miles, CD = 6 miles. Therefore BD = BC + CD = (6 + x) miles
DE = 8 miles, AB = 12 miles
Therefore:
[tex]\frac{BC}{BD}=\frac{DE}{AB}\\\frac{x}{x+6}=\frac{8}{12}\\48 + 8x = 12x\\ 12x-8x=48\\4x=48\\ x=48/4=12\\x=12miles[/tex]
