Agolden rectangle is a rectangle whose length is approximately 1.6 times its width. the early greeks thought that a rectangle with these dimensions was the most pleasing to the eye and examples of the golden rectangle are found in many early works of art. for example, the parthenon in athens contains many examples of golden rectangles. mike hallahan would like to plant a rectangular garden in the shape of a golden rectangle. if he has 208 208 feet of fencing available, find the dimensions of the garden.

The dimentions of the rectangle will be:

width = 40 ft

length = 64 ft

Step-by-step explanation:

The perimeter of the rectangle must equal the length of the fencing available.

*See the attached image*

The perimeter of the rectangle is:

P = 2*(width + length)

Since the rectangle must have the shape of a golden rectangle:

length = 1.6 width

Therefore:

P = 2*(1.6*width+ 1*width)= 2*(2.6 * width) = 5.2 width

Now, the perimeter must equal the length of the fencing, that is:

P = 208 ft = 5.2 width

Therefore:

width = (208/5.2) feet = 40 feet

and the length of the rectangle will be:

length = 1.6 width = 64 feet

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