Question

How do you find the dimensions of a rectangle given the perimeter?

Answer 1

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$2 \times l + b$
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Answer 2

Let ABCD be a rectangle in a given circle of radius a with centre at O. Let AB = 2x and AD = 2y be the sides of the rectangle. Then,

AM2 + OM2 = OA2  [ Δ OAM is a right angles triangle]

⇒ x2 + y2 = a2



Let P be the perimeter of the rectangle ABCD. Then,

P = 4x + 4y





For maximum or minimum, values of P, we have



Now, 



Thus, P is maximum when 

Putting  in (1), we obtain . Therefore, 

Hence, P is maximum when the rectangle is square of side