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Asked by sanrachna | 7th Nov, 2009, 04:53: PM

Expert Answer:

Draw a paralleligram with its longer side a and smaller side b. Let h be the height of the parallelogram and d1 and d2 be the two diagonals (refer fig).

Using pythagoras theorem, we have

(d1)2 = (a + x)2 + h2         .............(1)

(d2)2 = (a - x)2 + h2          ..............(2)

Adding (1) and (2), we have

d12  +  d2= (a + x)2 + h2  + (a - x)2 + h2

                     = 2a2 + 2h2 +2x2

                     =  2a2 + 2 (h2 +x2)

                    = 2a2 + 2b2

Hence the answer. 

 

Answered by  | 12th Nov, 2009, 01:18: PM

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