a farmer will build a rectangular pen for his sheep. a wall will form one side of the pen. the farmer has 28 m of fencing to form the other three sides. the farmer plans to build the pen so that it has its maximum possible area. what will be the dimensions of the farmer’s sheep pen? enter your answers in the boxes.
_ m by _ m

Question

contestada

Respuesta :

Kit929 Kit929 · Answer 1 · 2021-05-22T01:46:45+02:00

Answer:

14m by 7m

Step-by-step explanation:

thats the answer

Answer Link

facundo3141592 facundo3141592 · Answer 2 · 2022-05-18T11:21:31+02:00

The dimensions that maximize the area is a length of 14m and a width of 7m.

For a rectangle of dimensions L and W, the area is:

A = L*W

In this case, we assume L > W, and then one of the sides that measures L is the side where we will use the wall (so we save more of the fencing).

Then for the other 3 sides we use the 28 m of fencing, we will have:

28m = 2*W + L

Isolating L we get:

L = 28m - 2*W

And now we want to maximize the area, so first we can write:

A = L*W = (28m - 2*W)*W

A = 28m*W - 2*W^2

This is a quadratic function, where the vertex is the maximum, it happens at:

W = -28m/(2*-2) = 7m

So the width must be 7m, and the length is:

L = 28m - 2*7m = 14m

If you want to learn more about area:

https://brainly.com/question/24487155

#SPJ5