Question

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

A

l216

B

l28

C

l24

D

l22

Solution

The correct option is A l216 As per the question, 2(b+x)=l ⇒b=l2−x Now, area, A=xb=x(l2−x)=lx2−x2 For A to be maximum, dAdx=0⇒x=l4 and b=l4 Hence, (Area)max=l4×l4=l216

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