COMEDK · Maths · 27. Application of Derivatives
If the length of the diagonal of a square is increasing at the rate of \(0.1 \mathrm{~cm} / \mathrm{sec}\).
What is the rate of increase of its area when the side is \(\dfrac{15}{\sqrt{2}} \mathrm{~cm}\) ?
- A \(3 \mathrm{~cm}^2 / \mathrm{sec}\)
- B \(1.5 \mathrm{~cm}^2 / \mathrm{sec}\)
- C \(3 \sqrt{2} \mathrm{~cm}^2 / \mathrm{sec}\)
- D \(0.15 \mathrm{~cm}^2 / \mathrm{sec}\)
Answer & Solution
Correct Answer
(B) \(1.5 \mathrm{~cm}^2 / \mathrm{sec}\)
Step-by-step Solution
Detailed explanation
Let \(a\) be the side length and \(d\) be the diagonal of the square. The relationship between the diagonal and the side is \(d = a\sqrt{2}\), which implies \(a = \dfrac{d}{\sqrt{2}}\). The area \(A\) of the square is given by \(A = a^2\). Substituting…
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