COMEDK · Maths · 27. Application of Derivatives
The two equal sides of an isosceles triangle with a fixed base 'b' cm are decreasing at the rate of \(4 \mathrm{~cm} / \mathrm{sec}\). The rate at which the area is decreasing when each of the equal sides becomes equal to the base is
- A \(\dfrac{4 b}{\sqrt{3}}\)
- B \(\dfrac{4 b}{3}\)
- C \(4 \sqrt{3} b\)
- D \(\dfrac{2 b}{\sqrt{3}}\)
Answer & Solution
Correct Answer
(A) \(\dfrac{4 b}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
Let the equal sides of the isosceles triangle be \(x\) and the base be \(b\). The height \(h\) of the triangle is given by \(h = \sqrt{x^2 - (b/2)^2} = \sqrt{x^2 - b^2/4}\). The area \(A\) of the triangle is…
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