Prove that in any square pyramid, the squares of the height, slant he

1.	Prove that in any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.
Answer» Height = h, Slant height = l, Lateral edge = e \(l^2=h^2+(a/2)^2-(1)\) \(l^2=e^2-(a/2)^2-(2)\) (1) + (2) : 2l² = h² + e² \(l^2=\frac{h^2+e^2}{2}\) ∴ (h², I², e²) are in arithmetic sequence.

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

Answer»

Height = h,

Slant height = l,

Lateral edge = e

\(l^2=h^2+(a/2)^2-(1)\)

\(l^2=e^2-(a/2)^2-(2)\)

(1) + (2) : 2l² = h² + e²

\(l^2=\frac{h^2+e^2}{2}\)

∴ (h², I², e²) are in arithmetic sequence.

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

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