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

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: The dimensions of the garden are: Width=15 feet and Length=24 feet.