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Question

How can a string of length l be made into a rectangle so as to maximize the area of the rectangle?



Correct Answer
A

l216

Your Answer
B

l28

Your Answer
C

l24

Your Answer
D

l22


Solution

The correct option is A

l216



As per the question, 2(b+x)=l
b=l2x
Now, area, A=xb=x(l2x)=lx2x2
For A to be maximum, dAdx=0x=l4 and b=l4
Hence, (Area)max=l4×l4=l216

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