CUET · MATHS · PYQ PAPER 2023
The sides of an equilateral triangle are increasing at the rate of 2 cm/s. The rate at which the area increases, when side is 10 cm is:
- A \(\frac{10}{3} cm^2 / s\)
- B \(20 \sqrt{5} cm^2 / s\)
- C \(10 \sqrt{3} cm^2 / s\)
- D \(10 cm^2 / s\)
Answer & Solution
Correct Answer
(C) \(10 \sqrt{3} cm^2 / s\)
Step-by-step Solution
Detailed explanation
\(A = \frac{\sqrt{3}}{4} s^2\) \(\frac{dA}{dt} = \frac{\sqrt{3}}{2} s \frac{ds}{dt}\) \(\frac{dA}{dt} = \frac{\sqrt{3}}{2} (10) (2) = 10 \sqrt{3} \text{ cm}^2/\text{s}\)
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