DE || BC and AD+DB = 3+5. If AC= 5.6, find AE. ALso if AC= 4.8cm, find AE

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$G i v e n : i n t r i a n g l e △ A B C, D E ∥ B C, A D + D B = 3 + 5, A C = 5.6 W e k n o w t h a t, I f a l i n e i s d r a w n p a r a l l e l t o o n e s i d e o f t r i a n g l e i n t e r s e c t i n g t h e o t h e r t w o s i d e s, t h e n i t d i v i d e s t h e t w o s i d e s i n t h e s a m e r a t i o . i . e ., \frac{A D}{D B} = \frac{A E}{A C} \Rightarrow \frac{3}{5} = \frac{A E}{A C - A E} \Rightarrow \frac{3}{5} = \frac{A E}{5.6 - A E} \Rightarrow 16.8 - 3 A E = 5 A E \Rightarrow A E = 2.1 c m I f A C = 4.8 c m, t h e n \frac{3}{5} = \frac{A E}{A C - A E} \Rightarrow \frac{3}{5} = \frac{A E}{4.8 - A E} \Rightarrow 14.4 - 3 A E = 5 A E \Rightarrow A E = 1.8 c m$
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