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the area of a rectangle is 72 cm2. state the dimensions of the rectangle with the least perimeter. calculate the perimeter.

The least perimeter of the rectangle will be 24√2 cm.

Step-by-step explanation:

The area of a rectangle is given by, A = lw = 72 cm² {Given} ........... (1)

Here, l is the length of the rectangle and w is its width.

Now, perimeter of the rectangle is given by, P = 2l + 2w

⇒ ........... (2) {From equation (1)}

Now, condition for least perimeter is  

{Differentiating equation (2) both sides with respect to w}

⇒ w² = 72

⇒ w = 6√2 cm. {Since w can not be negative}

So, from equation (1) we get,

l = 6√2 cm.

Therefore, the least perimeter of the rectangle will be, P = 2(w + l) = 24√2 cm. (Answer)

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