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}


Step 3: Find the unknown value by using the basic proportional theorem.

              EXAMPLE:  from the given figure \frac{AL}{LC}=\frac{BM}{MC}  [since ( \frac{AD}{DB} = = \frac{AE}{EC} ]

                                 Write the formula in known lengths  

                                              \frac{AL}{AC-AL}=\frac{BM}{BC\ -\ BM}  

                                Substitute given equations in the above formula

                                             \frac{x - 3}{2x - (x -3)} = \frac{x - 2}{(2x + 3) - (x -2)}

                                                \frac{x - 3}{x + 3} = \frac{x -2}{x + 5}

                                             Cross multiply

                                 (x − 3) (x + 5) = (x − 2) (x + 3)

                                 x^2 + 2x - 15 = x^2 + x - 6

                                2x − x = − 6 + 15

                                         x = 9