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Yesterday i solved a problem which is: "A lamina in the shape of a rectangle whose length is 3 times its width expands by heat such that it preserves its shape with the same ratio between its dimensions. Find the rate of change in its area when its length equals 23 cm."

i solved it as follows: width = $x$ and length = $3x$, so the area will be $3x^2$ And now differentiating we get $6x$, and substituting for the value of the $x$ wich is $3x=23$ so $x=\frac{23}{3}$ so finally the answer will be $46$.

And my friend said I'm wrong, and he solved it as follows: length = $x$ and width = $\frac{x}{3}$, so the area will be $\frac{x^2}{3}$ after differentiation we get $\frac{2}{3}x$ and now simply substituting for x which is the length we get $\frac{46}{3}$

Who is right?! and why I'm wrong?

Mohaimn Draz
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    The rate of change of the length should be given but I can't see that in the question. Therefore I don't think it can be solved. – Mc Cheng May 27 '16 at 14:05
  • Note that both the length and width are functions of time. Both you and your friend should be differentiating with respect to time. To do so, we need to know $l'(t)$. The way you approached the problem, we would need to use $l'(t)$ to determine $w'(t)$. – N. F. Taussig May 27 '16 at 14:12

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