Algebra 2 Word Problem

Question

For the most pleasing effect, the ratio of the width of a rectangle to its length should equal the ratio of its length to the sum of its length and width. With this "Divine Proportion" in mind, design a rectangular picture frame with a perimeter of 60 centimeters. Give the dimensions to the nearest tenth of a centimeter.

 

I have no clue where to start or what to do.

Answer 1

Actually, I think the "Divine Proportion" is the Golden Ratio, which approximately equals 1.618. This is found from the Fibonacci Sequence: 1,1,2,3,5,8,13,21,34,55,...

Keep dividing a number by the number that precedes it: 1/1=1, 2=1=2, 3/2=1.5, 8/5=1.6, 13/8=1.625, 21/13=1.615, 34/21=1.619

The width and length relate this way:

l/w = (w+l)/l

So,  l/w=1.618    and l = 1.618w

P = 2l + 2w

60 = 2(1.618w) + 2w

60 = 3.236w + 2w

60 = 5.236w

w = 11.5 cm

l = 1.618(11.5)

l = 18.5 cm