Given AB | | DE. Triangle A B C. Side A B is 12 miles and B C is x miles. Triangle C D E. Side C D is 6 miles and D E is 8 miles. Sides A B and D E are parallel. What is the distance of BC? ΔABC ∼ ΔEDC 1. Proportion: 12 8 = x 6 2. Cross-multiply: 72 = 8x 3. Solve: BC = miles

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]

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