Rectangle ACEF is a golden rectangle. If side AC is 4 inches, can the smaller rectangle BDEF also be a golden rectangle?
A) Yes
B) No

Question

Rectangle ACEF is a golden rectangle. If side AC is 4 inches, can the smaller rectangle BDEF also be a golden rectangle? 
A) Yes 
B) No

Quizplus · Accepted Answer

A golden rectangle has the property that the ratio of the longer side to the shorter side is equal to the golden ratio, which is approximately 1.618. Since rectangle ACEF is a golden rectangle with side AC being 4 inches, the length of side AF is 4*1.618 = 6.472. Now, if we let the length of side BF be x, then we know that the length of side BD is also x (since rectangle BDEF is a rectangle). Therefore, the ratio of the longer side (AF) to the shorter side (BF) of rectangle BDEF is (6.472 + x)/x. If this ratio is also equal to the golden ratio of approximately 1.618, then we have:

(6.472 + x)/x = 1.618

Solving for x gives:

x = 3.961

Therefore, rectangle BDEF can also be a golden rectangle with side BF being approximately 3.961 inches.

Rectangle ACEF Is a Golden Rectangle