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In any square pyramid, which of the following squared quantities are in arithmetic progression?
AThe squares of the height, slant height and lateral edge
BThe squares of the slant height, half-base edge and lateral edge
CThe squares of the base edge, slant height and lateral edge
DThe squares of the base perimeter, lateral edge and height
Answer & Solution
Correct answer: A. The squares of the height, slant height and lateral edge
1. From half-base-edge a/2, height h and slant height l: l² = h² + (a/2)².
2. From slant height l, half-base edge a/2 and lateral edge e: e² = l² + (a/2)².
3. Adding both gives l² + e² = h² + 2(a/2)² + l², so e² - l² = (a/2)² and l² - h² = (a/2)².
4. The differences e² - l² and l² - h² are equal — i.e. h², l², e² form an arithmetic progression.
5. So the squares of height, slant height and lateral edge are in arithmetic sequence.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7-8 (pp 180-199, 2019 ed.)._
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