Krishna
0

Step 1: Understand the question and note down the given values

          

Step 2 : Select the appropriate theorem using the given data.

            THEOREM: (Basic proportional theorem)

              If a line is drawn parallel to one side of a triangle to intersect

              the other two sides in distinct points, then the other two sides are divided

            in the same ratio.

              Given : In ∆ABC, DE || BC which intersects sides AB and

            AC at D and E respectively.

                So, \frac{AD}{DB} = = \frac{AE}{EC} = \frac{3}{5}


Step 3: Find the unknown lengths (AE) by using the basic proportional theorem  

              EXAMPLE:   \frac{AE}{EC} = \frac{3}{5}  [since ( \frac{AD}{DB} = = \frac{AE}{EC} ]

                                We can write  EC =  AC - AE substitute this in the above equation

                                               \frac{AE}{AC - AE} = \frac{3}{5}   

                                Plugging the AC = 5.6(given) in the above equation

                                                 \frac{AE}{5.6 - AE} = \frac{3}{5}

                                               5AE = 3 (5.6 - AE)

                                               5 AE + 3 AE = 3(5.6)

                                                     AE = \frac{16.8}{8}

                                                    AE = 2.1 cm