In a triangle ABC, D and E are two points on sides AB and AC, respectively, such that DE is parallel to BC and AD : DB = 3 : 5. If AC = 5.6 cm, then find the value (in cm) of AE.
2.1
Since DE is parallel to BC, the triangle ADE is similar to triangle ABC by the Basic Proportionality Theorem (Thales' theorem).
Given that AD : DB = 3 : 5, the ratio of AD to the entire AB is:
AD ÷ AB = 3 ÷ (3 + 5) = 3 ÷ 8.
Similarly, AE ÷ AC = 3 ÷ 8 (since the triangles are similar).
AE = (3÷8) × 5.6 = 2.1 cm.
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