Question

Classical mathematics uses the term "Golden Ratio" for the ratio (1 + √ 5) : 2 . The Golden Ratio was used by many famous artists to determine the dimensions of their paintings. If the ratio of the length to the width of a painting is (1 + √ 5) : 2 , find the length, in feet, of a painting that has a width of 14 feet. Express your answer in simplest radical form.

Answer 1

\[l/w = (1+\sqrt {5})/2\]
\[l/14 = (1+\sqrt {5})/2\]
\[l = 14(1+\sqrt {5})/2 = 7(1+\sqrt {5})\]

Answer 2

yay i got that, just wanted to check my answer . i got 14 +7√ 5

Answer 3

if you expand the answer I gave, then it comes to \[7 + 7\sqrt {5}\]not\[14+7\sqrt {5}\]