Asked by Sarah
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.
Answers
Answered by
Ryan
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
Your answer rounded would be 7.4
Answered by
Bosnian
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
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