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In fig , XY || seg AC.If 2AX = 3BX and XY = 9. Complete the activity to find the value of AC.

Activity : 2AX = 3BX  \({AX \over BX } = {.....\over ....}\) 

             \({ AX +BX \over BX}={.....+.......\over.....}\)                   ... by componendo.

              \({AB \over BX} = {.... \over ..... }\)                              .. (I)

             \(\Delta\) BCA ~ \(\Delta\) BYX                            ....... test of similarity.

           \( { BA \over BX} ={ AC \over XY} \)                            ... corresponding sides of similar triangles.

              \({.... \over .... }= {AC \over 9}\)

              AC = ....                                                 ... from (I)

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Sol:       

             2AX = 3BX 

               \({AX \over BX } = {3\over 2}\) 

             \({ AX +BX \over BX}={3+2\over2}\)                   ... by componendo.

              \({AB \over BX} = {5 \over 2 }\)                              .. (I)

            \(\Delta\) BCA ~ \(\Delta\)BYX                            ....... test of similarity.

              \( { BA \over BX} ={ AC \over XY} \)                            ... corresponding sides of similar triangles.

              \({5\over 2 }= {AC \over 9}\)

              AC = 22.5                                                 ... from (I)

Similarity August 22 , 2018 0 Comments 63 views