The result you need is that for a rectangle with a given perimeter the square has the largest area. So with a perimeter of 28 feet, you can form a square with sides of 7 feet and area of 49 square feet.

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Similarly one may ask, how do you find the maximum area of a rectangle with a fixed perimeter?

A rectangle will have the maximum possible area for a given perimeter when all the sides are the same length. Since every rectangle has four sides, if you know the perimeter, divide it by four to find the length of each side. Then find the area by multiplying the length times the width.

Similarly, what are the dimensions of the rectangle with maximum area? The largest possible area is 1024 square meters Then the length and width are the same: 32 meters. What do you call a rectangle that is as wide as it is long? A square.

Besides, what shape has the largest area to perimeter ratio?

circle

What is a fixed perimeter of a rectangle?

This means the length of the side of an area, a rectangle for example, is always the same : If the side of the rectangle are a and b, then a+b times two is fixed, or, which is the same, the sum a and b is fixed.

Related Question Answers

How do you find the perimeter with the area?

You can calculate the area of a square by using both the length of one side and its perimeter. Divide the perimeter length by 4 to get the measurement for each side of the square. For example, a square with a perimeter of 20 inches has four sides of five inches each. Multiply the length of one side by another side.

How do you find the minimum and maximum area of a rectangle?

To find the minimum possible area, subtract the greatest possible error from each measurement, then multiply. The minimum possible area is 22.75 square miles. The maximum possible area is 33.75 square miles. The rectangle below is labeled with its measured dimensions.

Which shape covers the most area?

Given the belief that the circle gives the largest area, we expect that for any shape, This is known as the isoperimetric inequality.

What shape has the highest surface area?

We can use the concept that for a given volume, the surface area is minimum for a shape with maximum sides that is a sphere and for maximum surface area we need minimu sides. So I guess it will be tetrahedron with 4 sides.

Does a circle or square have more area?

The area of a square is s² , where s is the side length. But s = P/4, so the area of a square is P² /16. Since 1/(4π) > (1/16), the circle has more area than the square. Since this is less than 1/(4π), the circle has more area than the octagon.

What shape has the largest perimeter?

rectangle

Is area always larger than perimeter?

Area is length x breadth = 1x t = t. Now 2 + 2t is always greater than t. Therefore here PM > A, when s =1. This means whenever you have one of the sides as 1, perimeter will be always (numerically) greater than area.

What percentage of a square is a circle?

78.5%

Is a square and a circle the same?

This question is hard to understand! A square with side length 2 and a circle share the same center. That's fine. The total area of the regions that are inside the circle and outside the square is equal to the total area of the regions that are outside the circle and inside the square.

Why does a square have more area than a rectangle?

Because they have the same perimeter we can say A+B=2C. so the area of the square will be greater than that of the rectangle by the square of difference of the sides length.

What is the maximum area of a rectangle?

The area of a rectangle is the length times the width and with the given amount of fencing you have you get the maximum area if the length and width are equal, that is the shape of the garden is a square. To one decimal place that's 90.3 square metres.

What are dimensions of a rectangle?

Dimensions for a Rectangle. Write down the area equation: A = L * W where "A" stands for the area, "L" stands for the length and "W" stands for the width of a rectangle. Solve the area equation: 30 = L * 6. Divide both sides of the equation by 6, and write down the answer. It will look like this: 5 = L.

How do we find the perimeter of a rectangle?

To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height, then you can easily find all four sides (two sides are each equal to the height and the other two sides are equal to the width). Multiply both the height and width by two and add the results.

How do you find the dimensions of a rectangle given the area?

The area of a rectangle (A) is related to the length (L) and width (W) of its sides by the following relationship: A = L ⋅ W. If you know the width, it's easy to find the length by rearranging this equation to get L = A ÷ W. If you know the length and want the width, rearrange to get W = A ÷ L.

Is the maximum area of a rectangle a square?

Thus, the rectangle with maximum area is a square. - (P - 4x)/2 = 0 yields x = P14 = y. The answer is a square.

What is the formula for area?

The most basic area formula is the formula for the area of a rectangle. Given a rectangle with length l and width w, the formula for the area is: A = lw (rectangle). That is, the area of the rectangle is the length multiplied by the width.

Can a rectangle be a square?

A rectangle can be tall and thin, short and fat or all the sides can have the same length. Thus every square is a rectangle because it is a quadrilateral with all four angles right angles. However not every rectangle is a square, to be a square its sides must have the same length.

What is a fixed perimeter?

This means the length of the side of an area, a rectangle for example, is always the same : If the side of the rectangle are a and b, then a+b times two is fixed, or, which is the same, the sum a and b is fixed.