CBSE 2025 · Region 1 · Set 2 · Q28 · 3 marks
The area of an expanding rectangle is increasing at the rate of $\displaystyle 48 \mathrm{~cm}^{2} / \mathrm{s}$. The length of the rectangle is always square of its breadth. At what rate the length of rectangle increasing at an instant, when breadth $\displaystyle =4.5 \mathrm{~cm}$ ?
Marking-scheme solution
Let the length and breadth of the expanding rectangle at any time be ' $\displaystyle x$ ' and ' $\displaystyle y$ ' respectively.
Then, $\displaystyle x=y^{2}, A($ Area $\displaystyle )=x y=x^{\frac{3}{2}}$
\[\frac{d A}{d t}=\frac{3}{2} \sqrt{x} \frac{d x}{d t}
\]
$\displaystyle \Rightarrow 48=\frac{3}{2} \sqrt{(4.5)^{2}} \frac{d x}{d t} \Rightarrow \frac{d x}{d t}=\frac{64}{9} \mathrm{~cm} / \mathrm{s}$
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CBSE Class 12 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.