Question

A golden 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.

Answer 1

The dimentions of the rectangle will be:

width = 40 ft

length = 64 ft

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