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 7878 feet of fencing available, find the dimensions of the garden.

Question

Mathematics

Brycen Koch

12 April, 17:47

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 7878 feet of fencing available, find the dimensions of the garden.

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Anne Gentry · Answer 1

Mike has 78 feet of fencing available for his garden, this is the perimeter (P) of the rectangle:

Perimeter: P=78 feet

The formula of Perimeter is:

P=2 (W+L), where W is the width and L is the length, then:

P=78→2 (W+L) = 78

Dividing both sides of the equation by 2:

2 (W+L) / 2=78/2

W+L=39

If the shape is of a golden rectangle, we know:

L=1.6W

Replacing this above:

W+1.6W=39

Adding similar terms:

2.6W=39

Solving for W

2.6W/2.6=39/2.6

W=15 feet

L=1.6W=1.6 (15) →L=24 feet

Answer: T he dimensions of the garden are: Width=15 feet and Length=24 feet.