If you look up golden rectangle you will see that the ratio is 1.618 so just divide 12 by 1.618.
Your answer rounded would be 7.4
A car fits onto a golden rectangle with a length of 12 ft. What is the cars width? Write your answer in simplified radical form and rounded to the nearest tenth of a foot.
2 answers
A golden rectangle is a rectangle whose side lengths are in the golden ratio:
phi = 1 / [ ( 1 + sqroot 5 ) / 2 ]
W = L * phi
W = 12 * 1 / [ ( 1 + sqroot 5 ) / 2 ] =
12 * 2 / ( 1 + sqroot 5 ) =
24 / ( 1 + sqroot 5 ) =
24 / ( 1 + 2.236068 ) =
24 / 3.236068 = 7.416408 ft
W = 7.4 ft rounded to the nearest tenth
Remark :
phi in equations mean greek letter phi
phi = 1 / [ ( 1 + sqroot 5 ) / 2 ]
W = L * phi
W = 12 * 1 / [ ( 1 + sqroot 5 ) / 2 ] =
12 * 2 / ( 1 + sqroot 5 ) =
24 / ( 1 + sqroot 5 ) =
24 / ( 1 + 2.236068 ) =
24 / 3.236068 = 7.416408 ft
W = 7.4 ft rounded to the nearest tenth
Remark :
phi in equations mean greek letter phi