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.
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
A golden rectangle is defined as a rectangle whose side lengths are in the ratio of the golden ratio, approximately 1.618.
Let's assume the width of the car is "x" feet.
According to the given information, the length of the golden rectangle is 12 ft.
The ratio of the length to the width in a golden rectangle is 1.618, so we can set up the following equation:
12 / x = 1.618
To find the width of the car, we can solve for "x" by cross-multiplication:
12 = 1.618x
Divide both sides of the equation by 1.618:
x = 12 / 1.618
Using a calculator, we find that x is approximately 7.41 (rounded to two decimal places).
Therefore, the width of the car, in simplified radical form and rounded to the nearest tenth of a foot, is approximately √(7.41^2) = 8.0 ft.
To find the width of the car, we can use the properties of a golden rectangle. A golden rectangle is a rectangle in which the ratio of the longer side to the shorter side is equal to the golden ratio, which is approximately 1.618.
The formula for the golden ratio states that if the longer side has a length of L, then the shorter side has a length of L/1.618.
In this case, we are given the length of the rectangle, which is 12 ft. Using the golden ratio formula, we can find the width.
Width = Length / 1.618
= 12 ft / 1.618
≈ 7.4167 ft
Rounding this answer to the nearest tenth of a foot, we get approximately 7.4 ft.
So, the width of the car is approximately 7.4 ft.
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