If-you-had-a-rectangle-with-side-lengths-h-and-b-the-area-is-given-by-A-h-b-hb-If-I-were-to-change-increase-or-decrease-the-value-of-one-or-both-of-the-variables-in-A-how-can-I-write-the-chang

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Question Number 3330 by Filup last updated on 11/Dec/15

$$\mathrm{If}\mathrm{you}\mathrm{had}\mathrm{a}\mathrm{rectangle}\mathrm{with}\mathrm{side}\mathrm{lengths}$$$$h\mathrm{and}b,\mathrm{the}\mathrm{area}\mathrm{is}\mathrm{given}\mathrm{by}:$$$$A(h,b)=hb$$$$$$$$\mathrm{If}\mathrm{I}\mathrm{were}\mathrm{to}\mathrm{change}\left(\mathrm{increase}\mathrm{or}\mathrm{decrease}\right)$$$$\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{one}\mathrm{or}\mathrm{both}\mathrm{of}\mathrm{the}\mathrm{variables}$$$$\mathrm{in}A,\mathrm{how}\mathrm{can}\mathrm{I}\mathrm{write}\mathrm{the}\mathrm{change}\mathrm{in}\mathrm{area}?$$

Answered by Rasheed Soomro last updated on 11/Dec/15

$$A=hb$$$$Whenonevariablechanges$$$$Letbischangedby\delta bandcorrespondingchange$$$$inAisdenotedby\delta A$$$$A=hb\Rightarrow A+\delta A=h(b+\delta b)$$$$\Rightarrow \delta A=h(b+\delta b)-hb$$$$=hb+h\delta b-hb=h\delta b$$$$Whenbothvariableschange$$$$A=hb\Rightarrow A+\delta A=(h+\delta h)(b+\delta b)$$$$\Rightarrow \delta A=(h+\delta h)(b+\delta b)-hb$$$$=hb+h\delta b+b\delta h-hb$$$$=h\delta b+b\delta h$$

Commented by Filup last updated on 11/Dec/15

$$\mathrm{Awesome}!\mathrm{I}\mathrm{was}\mathrm{so}\mathrm{curious}\mathrm{as}\mathrm{to}$$$$\mathrm{how}\mathrm{you}\mathrm{would}\mathrm{write}\mathrm{it}!\mathrm{Good}\mathrm{job}!!!$$

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