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,

h^{2}_{,} s^{2} and e^{2} are in AP with,

First term, a= h^{2}

Common difference, d=

Hence, proved.

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