Practice free →
HomeKerala SSLC (Class 10)MathematicsPyramids › In any square pyramid, which of the following sq…

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.)._
Solve this in the app — Kerala SSLC (Class 10) practice & 24k+ MCQs →
Related questions