Answer:
<u>EC = 1 ft</u>
Step-by-step explanation:
DE // BC and AC and AD are transversal lines
∴ ∠E≅∠C ⇒ corresponding angles are congruent
∠D≅∠B ⇒ corresponding angles are congruent
∠A≅∠A ⇒ Reflexive property
∴Δ ADE is similar to ΔABC by AA postulate
So, The corresponding sides are in proportion.
![\frac{AC}{AE} = \frac{AB}{AD}](https://tex.z-dn.net/?f=%5Cfrac%7BAC%7D%7BAE%7D%20%3D%20%5Cfrac%7BAB%7D%7BAD%7D)
AE = 4 ft , AD = 8 ft , AB = 8 + 2 = 10 ft
AC = AE * AB/AD = 4*10/8 = 40/8 = 5 ft
EC = AC - AE = 5 - 4 = 1 ft
<u>So, the Length of EC = 1 ft.</u>