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Answer:
DE = 24/5 cm
Explanation:
Given :
DE ║ BC , AE = 8 cm , EC= 2 cm and BC = 6 cm
In triangle ADE and ABC
∠A = ∠A (it is common angle)
∠ADE = ∠ABC ( DE ║ BC, corresponding angles)
∠AEC = ∠ACB (DE ║ BC, corresponding angles)
By AAA similarity ΔADE similar to ΔABC
By CPST
=> AE/AC = DE/BC
=> 8/10 = DE / 6 (AC = AE + EC = 8 + 2 = 10)
=> 4/5 = DE/ 6
=> DE = 24/5 cm
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