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Q: How do you find the optimal area of a rectangle given its perimeter?

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Assuming that you want to minimise the perimeter, then use a square. Its side length is, of course, given by the square root of the area.

You cannot.

The square is.

square

The perimeter of rectangle A would then be 80 because 80 to 100 is 4 to 5 simplified and the area of triangle A would depend on the sides and area of rectangle B which have not been given.

There is no formula for a rectangle. There are formula for calculating its area, perimeter or length of diagonals from its sides, or it is possible to calculate the length of one pair of sides given the other sides and the area or perimeter, or the two lots of sides given area and perimeter and so on.

In the case of a rectangle, you would maximize the area given the perimeter by making the dimensions equal. In other words, you would make the rectangle into a square. However, to truly maximize the area, you would make the perimeter a perfect circle.

The maximum area for a rectangle of fixed perimeter is that of the square that can be formed with the given perimeter. 136/4 = 34, so that the side of such a square will be 34 and its area 342 = 1156.

If you are given the area you will have to think what do you times with the number you have to get it.

Not at all. For example:A square of 2 x 2 will have a perimeter of 8, and an area of 4. A rectangle of 3 x 1 will also have a perimeter of 8, and an area of 3.A "rectangle" of 4 x 0 will also have a perimeter of 8, but the area has shrunk down to zero. The circle has the largest area for a given perimeter/circumference.

the area of a rectangleis 100 square inches. The perimeter of the rectangle is 40 inches. A second rectangle has the same area but a different perimeter. Is the secind rectangle a square? Explain why or why not.

The perimeter of the rectangle is the sum of its 4 sides.

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