Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Find the dimensions of a rectangle with area 3 square meters whose perimeter is as small as possible.

Sagot :

Numenius

Answer:

The perimeter is minimum for Length and width both are [tex]\sqrt3[/tex].

Step-by-step explanation:

Area, A = 3 square metre

Let the length is L and width is W.

Area = L W

3 = L W.....(1)

The perimeter is given by

P = 2 (L + W)

Substitute the value of  from (1)

[tex]P = 2 \left ( L +\frac{3}{L} \right )\\\\P = 2 L + \frac{6}{L}\\\\\frac{dP}{dL} = 2 - \frac{6}{L^2}\\\\Now\\\\\frac{dP}{dL}=0\\\\2 - \frac{6}{L^2} = 0\\\\L = \sqrt 3, W = \sqrt 3[/tex]

Now

[tex]\frac{d^2P}{dL^2}=\frac{12}{L^3}\\[/tex]

It is alays positive, so the perimeter is minimum.

We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.