Q. 3

Prove that in any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.

Answer :


In the diagram,


e = lateral edge


s = slant height


h = height of pyramid


l = side of square base


With the help of diagram given below we get that, diagonal of square base is of length l√2



From the figures and Pythagoras theorem,



(1)


Also,


(2)


By comparing (1) and (2) we get that,


h2, s2 and e2 are in AP with,


First term, a= h2


Common difference, d=


Hence, proved.


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