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..
Considering this, is the maximum area of a rectangle always a square?
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. This follows since given a positive number A with xy=A the sum x+y is smallest when x=y=√A.
Also, what is the maximum area of a rectangle? Approach: For area to be maximum of any rectangle the difference of length and breadth must be minimal. So, in such case the length must be ceil (perimeter / 4) and breadth will be be floor(perimeter /4). Hence the maximum area of a rectangle with given perimeter is equal to ceil(perimeter/4) * floor(perimeter/4).
Herein, why is the maximum area of a rectangle a square?
This implies that if a rectangle and a square have the same perimeter, the rectangle must have a smaller area. Let's says the rectangle has sides of length A and B and the square has sides of length C. so the area of the square will be greater than that of the rectangle by the square of difference of the sides length.
Is a rectangle 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.
Related Question Answers
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 is the area of rectangular?
To find the area of a rectangle, multiply the length by the width. The formula is: A = L * W where A is the area, L is the length, W is the width, and * means multiply. A square is a rectangle with 4 equal sides.Which triangle has maximum area?
equilateral
How do you find area?
To find the area of a rectangle multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.Can perimeter be greater than area?
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.Does bigger perimeter mean bigger area?
Thomas remarked: The perimeter is always bigger except for one (Shape G). The area and perimeter are the same. The same happened if there you have a rectangle that has a length of 6 and a width of 3.Do squares have the largest area?
Isoperimetric Theorem for Rectangles. A particular case of the Isoperimetric Theorem says that among all rectangles of a given perimeter, the square has the largest area. (This is of course equivalent to the claim that among all rectangles of a given area the square has the least perimeter.)Why are rooms rectangular?
The constraints of packing rooms together, and the flexibility of dimensioning allowed by rectangular arrangements, explain the predominance of the right angle in architectural plans. Why are most buildings rectangular? force of gravity. Floors are flat so that we, and pieces of furniture, can stand easily on them.Does a square have the same perimeter and area?
But if both the length and the width are odd, then the area will be odd, meaning that it is impossible for the perimeter to be the same as the area. Each square along the edges accounts for one unit of perimeter, except for the four corner squares. They account for two units of perimeter but only one unit of area.Can a square have the same area as a rectangle?
A square and a rectangle have the same area. A square and a rectangle have the same area. If the rectangle has a length of 25 cm and a perimeter of 82 cm, find the length of the square.What shape has the largest area to perimeter ratio?
Specifically, for a given area, the longest, skinniest rectangle has the greatest perimeter and the most ”square-like” rectangle has the least perimeter.How do you find a perimeter?
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.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.What is a area and perimeter?
Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.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 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 solve optimization problems?
To solve an optimization problem, begin by drawing a picture and introducing variables. Find an equation relating the variables. Find a function of one variable to describe the quantity that is to be minimized or maximized. Look for critical points to locate local extrema.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.What is maximum area of a rectangle?
A rectangle will have the maximum possible area for a given perimeter when all the sides are the same length. Then find the area by multiplying the length times the width. If you know the area and want to find the minimum perimeter possible, take the square root of the area to find the length of each side. 
