Answer:
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
⇒ [tex]P = 2(\frac{72}{w}) + 2w[/tex] ........... (2) {From equation (1)}
Now, condition for least perimeter is
[tex]\frac{dP}{dw} = 0 = - \frac{72 \times 2}{w^{2}} + 2[/tex]
{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)