Is length the longer side and breadth or width the shorter side?
In terms of length being the longer side of a rectangle, you may find an indirect answer to this interesting question by considering what is known as the golden rectangle:
Many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing (see Applications and observations below). Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which can be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets, in some cases based on dubious fits to data.
A golden rectangle with longer side a and shorter side b, when placed adjacent to a square with sides of length a, will produce a similar golden rectangle with longer side a + b and shorter side a. This illustrates the relationship \frac{a+b}{a} = \frac{a}{b} = 1.618.
For more about this, see
http://en.wikipedia.org/wiki/Golden_ratio
In terms of length being the longer side of a rectangle, you may find an indirect answer to this interesting question by considering what is known as the golden rectangle:
Many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing (see Applications and observations below). Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which can be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets, in some cases based on dubious fits to data.
A golden rectangle with longer side a and shorter side b, when placed adjacent to a square with sides of length a, will produce a similar golden rectangle with longer side a + b and shorter side a. This illustrates the relationship \frac{a+b}{a} = \frac{a}{b} = 1.618.
For more about this, see
http://en.wikipedia.org/wiki/Golden_ratio
I think in mathematics there is no distinction between longer side or smaller side. These are considered as the two sides of a rectangle. Area of rectangle = product of two adjacent sides . Perimeter of rectangle = sum of all sides . Diagonal of rectangle = square root of sum of the square of two sides. etc. We only give name to simplify our notation or formulas sake .......
Poonam,
Good post! Yes, you are correct. A rectangle with length and width is a special case.
That special case leads to the following formulas:
If a rectangle has length \ell and width w
it has area K = \ell w\,,
it has perimeter P = 2\ell + 2w = 2(\ell + w)\,,
each diagonal has length d=\sqrt{\ell^2 + w^2},
and when \ell = w\,, the rectangle is a square.
A more general view of rectangles is given in the attached pdf file.
Thanks James Peter for providing the pdf file of the more general view of rectangle.
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