Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

A rectangular garden 800 square feet in area is to be fenced off against rodents. Find the dimensions that will require the least amount of fencing if one side of the garden is already protected by a barn.

Sagot :

reinhard10158

Step-by-step explanation:

the area of a rectangle is

a × b

with a, b being the length and width (in any sequence).

a×b = 800

a = 800/b

the perimeter is

2a + 2b

one side is not needed, so we take one of them off. e.g. we take off one a.

a + 2b need to be a minimum

800/b + 2b

f(b) = 800/b + 2b

the extreme value(s) we find as the zero points of the first derivative.

f'(x) = -800/(b²) + 2 = 0

2 = 800/(b²)

2b² = 800

b² = 400

b = ±20 ft

negative lengths don't make sense, so, 20 ft is the solution.

a×b = 800

a×20 = 800

a = 40 ft

so, the minimum fencing is for

a = 40 ft

b = 20 ft (2 times)

the second a is covered by the barn.

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.