Question

In a triangle ABC ,DE//BC IF AD=DB=3.5and AC=4.8.find AE

Answer 1

In ΔABC:

Since DE║BC,

So, by Basic Proportionality Theorem:

⇒AD/DB=AE/EC

⇒AD/DB=AE/AC-AE                                [∵AE+EC=AC]

∴Putting values:

⇒3.5/3.5=AE/4.8-AE

⇒ 1 =AE/4.8-AE                                 [∵3.5/3.5=1]

∴ 4.8-AE = AE                                    [Transposing 4.8-AE from RHS to LHS]

⇒ 4.8= AE+AE

⇒ 4.8= 2AE

⇒ AE= 4.8/2   ⇒ AE=2.4

Hope this helps.