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NCERT Class 12 · Ch 6 Miscellaneous Exercise · Q2

NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Miscellaneous Exercise Question 2

The equal sides of an isosceles triangle with fixed base b shrink at 3 cm/s. Find the area-decrease rate when each equal side equals b.
Instant when equal sides equal the base
Instant when equal sides equal the base

💡 Concept Hints

  1. Identify the domain and the inner and outer functions, or the relevant one-sided limits.
  2. Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.

✅ Step-by-Step Solution

Final Answer: Area rate −√3 b cm²/s; decrease magnitude √3 b cm²/s.
  1. Let each equal side be u, so height H=√(u²−b²/4) and area A=(b/2)√(u²−b²/4).
  2. Differentiate in time: Aₜ=(bu/[2√(u²−b²/4)])uₜ.
  3. At u=b and uₜ=−3, the height is √3b/2, hence Aₜ=−√3b.

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