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a rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a wire fence. using 100 meters of fencing, what is the largest rectangular region that can be enclosed? give both the dimensions and the area.



Answer :

Dimensions of the rectangular plot are 25' × 50'.

The area of a rectangular plot is 1250m.

What is the dimension of the rectangle?

Four perpendicular sides make up the two-dimensional geometric shape of a rectangle. Two of the four sides are distinct, and the other two resemble the distinctive sides. The dimensions of a rectangle are these two distinctive sides.

Here, we have

100 meters fencing

We have to find the dimensions and area of the rectangular plot.

so, 2x + y = 100

y = 100 - 2x

A = xy

A = x (100 - 2x)

A = 100x - 2x²

We differentiate w.r.t x, and we get

A' = 100 - 4x

We put, A'= 0

100 - 4x = 0

x = 25

y = 50

A = xy

A = 25 × 50

A = 1250m

Hence, the dimension of the rectangular plot is 25' × 50'.

The area of a rectangular plot is 1250m.

To learn more about the dimensions from the given link

https://brainly.com/question/26740257

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