Question

you are asked to fence a rectagular region and maximize the area. you are given 260 meters of fencing materials. what should be the dimension of of the rectangular region

Answer 1

To maximize the area of a rectangular region with 260 meters of fencing, each side of the resulting square should be 65 meters, resulting in a maximum area of 4225 square meters.

Step-by-step explanation:

To maximize the area of a rectangular region with a given amount of fencing material, you want to use the fencing material to form a square, since the square has the largest area for a given perimeter compared to any rectangle. In this case, with 260 meters of fencing materials, to form a square each side should have a length of 260 meters divided by 4, because a square has four equal sides.

Step-by-step:

1. Divide the total length of fencing material by 4 to find the length of one side of the square.
2. Calculate the area of the square by squaring the length of one side.

If you have 260 meters of fencing material:

1. One side of the square: 260 meters / 4 = 65 meters.
2. Area of the square: 65 meters * 65 meters = 4225 square meters.