Entry level calculus question

Calculus Level 1

The perimeter of a rectangle is 180 cm. What is its maximum possible area in sq cm?


The answer is 2025.

Arkajyoti Banerjee by Arkajyoti Banerjee , 20, India

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1 solution

Let the length of the rectangle be l, and its breadth b. Then its perimeter = Subsequently, its area = We know that a function is maximized when its derived function equals 0. Then the value of b for which its area will be maximum is: Therefore, l = 90-45 = 45 cm. Its max area = lb = 45 cm × 45 cm = 2025 sq cm

3 Helpful 0 Interesting 1 Brilliant 0 Confused

Or you could use A M ≥ G M AM\geq GM directly since both l , b l,b are positive reals ...

Rishabh Jain - 5 years, 3 months ago

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Did it the same way! :P

Harsh Khatri - 5 years, 3 months ago

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Yet again...... ;-)

Rishabh Jain - 5 years, 3 months ago

I did it from the basic level so that calculus beginneers can understand it properly. Still, nice approach.

Arkajyoti Banerjee - 5 years, 3 months ago

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