CBSE 2023 · Region 2 · Set 3 · Q23 · 2 marks
If equal sides of an isosceles triangle with fixed base $\displaystyle 10$ cm are increasing at the rate of $\displaystyle 4 \mathrm{~cm} / \mathrm{sec}$, how fast is the area of triangle increasing at an instant when all sides become equal? $\displaystyle 2$
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"Marking-scheme solution
Let the equal side be ' $\displaystyle x$ ', then $\displaystyle \frac{d x}{d t}=4 \mathrm{~cm} / \mathrm{s}$\begin{aligned}
& A=5 \sqrt{x^{2}-25} \Rightarrow \frac{d A}{d t}=\frac{5 x}{\sqrt{x^{2}-25}} \frac{d x}{d t}
& \left.\frac{d A}{d t}\right]_{x=10}=\frac{40}{\sqrt{3}} \mathrm{~cm}^{2} / \mathrm{s}
\end{aligned}
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CBSE Class 12 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.