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.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 2.1.
AC = 5.6 cm and AD : DB = 3 : 5
So, AD/DB = 3/5
Since DE is parallel to BC, triangles ADE and ABC are similar.
Thus, AD/DB = AE/EC = 3/5
Let AE = x, then EC = AC - AE = 5.6 - x
According to the similarity ratio, AD/DB = AE/EC
⇒ x/(5.6 - x) = 3/5
⇒ 3(5.6 - x) = 5x
⇒ 16.8 - 3x = 5x
⇒ 8x = 16.8
⇒ x = 16.8/8 = 2.1
Therefore, the value of AE is 2.1 cm.