Question

Hello everyone! Can you please help me? Help would be really really appreciated!

The area of a rectangle is 72 cm2. State the dimensions of the rectangle with the least perimeter. Calculate the perimeter.

Answer 1

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

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

⇒
`P = 2((72)/(w)) + 2w` ........... (2) {From equation (1)}

Now, condition for least perimeter is

`(dP)/(dw) = 0 = - (72 * 2)/(w^(2)) + 2`

{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)