Page 23 - Mathematics Class - X
P. 23

J                      G                                B
                                            I                                F   A

                                                A                        B
                                            H                                E
                            x
               A                        B







                                                                                                         C
                                                                                 D
                                            K                                P                             AHIJ BEFG
                                                D                        C
               D                        C      L  M                    N     O                            DKLM CNOP


                        Fig. (a)                         Fig. (b)                              Fig. (c)



          9.  Total area of Fig. (c) is 8 × 8 = 64 sq units or 60 + 4 sq units and area of Fig. (b) and Fig. (c) is same,
              i.e.             x  + 4x + 4 = 64
                                2
               and   (x)  + 2 (2 × x) + (2)  = 64
                                        2
                       2
                                  (x + 2)   = (8) 2               [Q  a  + 2(a)(b) + b  = (a + b) ]
                                                                       2
                                                                                     2
                                                                                               2
                                        2
              \                     x + 2 = ± 8
                                    x + 2 = 8                     (Taking +Ve)
                                           x = 6
              or                    x + 2 = – 8                   (Taking –Ve)

                                           x = – 10

               where, x represents the length of square, so we cannot take – 10 in this case, though it is also a solution of
              the equation.                                                             [Q length is always positive]


        OBSERVATIONS
        Solve various quadratic equations by making the squares as described above and obtain the solutions.


        INFERENCE
        We have obtained the solution of a quadratic equation (x  + 4x = 60) by completing the square geometrically.
                                                              2

        EXTENDED TASK
          1.  Solve various quadratic equations by making the squares as described above and obtain the solution(s).
          2.  Obtain the solution of a quadratic  equation  (for example,  x  + 10x = 24) by completing  the square
                                                                           2
              geometrically.


        APPLICATION
        Quadratic equations are useful to understand parabolic paths of projectiles in any direction.




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