CUET · MATHS · PYQ PAPER 2025
The sides of an equilateral triangle are increasing at the rate of \(2 cm / sec\). The rate at which the area increases when the side is 10 cm , is
- A \(20 \sqrt{3} cm^2 / sec\)
- B \(10 \sqrt{3} cm^2 / sec\)
- C \(3 \sqrt{5} cm^2 / sec\)
- D \(5 \sqrt{3} cm^2 / sec\)
Answer & Solution
Correct Answer
(B) \(10 \sqrt{3} cm^2 / sec\)
Step-by-step Solution
Detailed explanation
\(A = \frac{\sqrt{3}}{4} s^2\) \(\frac{dA}{dt} = \frac{\sqrt{3}}{2} s \frac{ds}{dt}\) \(\frac{dA}{dt} = \frac{\sqrt{3}}{2} (10)(2)\) \(\frac{dA}{dt} = 10 \sqrt{3} cm^2 / sec\)
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