A) 10 cm and 40 cm
B) 20 cm and 30 cm
C) 25 cm and 25 cm
D) 15 cm and 35 cm
Correct Answer: C
Solution :
\[2x+2y=100\Rightarrow x+y=50\] ?..(i) Let area of rectangle is A; \[\therefore A=xy\Rightarrow y=\frac{A}{x}\] Put in (i), we have \[x+\frac{A}{x}=50\Rightarrow A=50x-{{x}^{2}}\] Þ \[\frac{dA}{dx}=50-2x\] For maximum area \[\frac{dA}{dx}=0\] \[\therefore 50-2x=0\Rightarrow x=25\]and \[y=25\] Hence adjacent sides are 25 and 25 cm.
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