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50 POINTS!!

In the image below, DE∥BC. Find the measure of EC. Set up a proportion and solve for the measure. Show your work and label your answer

50 POINTSIn the image below DEBC Find the measure of EC Set up a proportion and solve for the measure Show your work and label your answer class=

Respuesta :

kudzordzifrancis

Answer:

1 ft

Step-by-step explanation:

From the diagram;

[tex]\triangle ADE\sim \triangle ABC[/tex]

Therefore

[tex]\frac{AB}{AD}=\frac{AC}{AE}[/tex]

Also, AB=8+2=10ft, AD=8ft, AE=4ft. We substitute to get:

[tex]\frac{10}{8}=\frac{AC}{4}[/tex]

Simplify to get:

[tex]AC = 5[/tex]

But AC=AE+EC

This implies that,

5=4+EC

EC=5-1

EC= 1 ft