Question

A wire of length \(64\) m is to be bent to form a rectangle such that its area is maximum, then its area is.....

• A. \(156\) sq.m
• B. \(324\) sq.m
• C. \(256\) sq.m
• D. \(320\) sq.m

Hint:

For a fixed perimeter the rectangle of maximum area is a square.

Answer 1

The Correct Option is C

Step 1: Use AM-GM
$lb\le\left(\frac{l+b}{2}\right)^2=16^2=256$, with equality when $l=b=16$. So the maximum area is $256$ sq. m.

Final Answer:
Option (C). \[ \boxed{\text{(C)}} \]