A farmer plans to enclose a rectangular pasture adjacent to a river (see figure). the pasture must contain 20,000 square meters in order to provide enough grass for the herd. no fencing is needed along the river. what dimensions will require the least amount of fencing?

Perpendicular to River = 100
Parallel to River = 200

Total Amount of Fencing = 400

*This specific problem, which shows up often, always has a side ratio of 1:2 when minimising fencing (or maximising area).

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maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-07-13T13:09:43+02:00

The dimensions for the fencing will be 200 meters and 100 meters for the least amount of fencing.

What is the area of the rectangle?

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

The figure is in the attached picture, please refer to the picture.

We have:

A farmer plans to enclose a rectangular pasture adjacent to a river the pasture must contain 20,000 square meters in order to provide enough grass for the herd.

Area of the rectangular pasture = 20,000 square meters

xy = 20,000

y = 20000/x, x > 0

Length of the fence = x + 2y

L = x + 2(20000/x)

L = x + 40000/x

L' = 1 - 40000/x² = 0

x = 200, x = -200(length cannot be negative)

x = 200

L''(200) > 0

At x = 200 meters fencings will require the least amount of fencing

y = 20000/200 = 100 meters

Thus, the dimensions for the fencing will be 200 meters and 100 meters for the least amount of fencing.

Learn more about the rectangle here:

https://brainly.com/question/15019502

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