If theres a golden rectangle, with one dimension shown as being 100, then what is the length of the unknown side? How do you do this please?
the golden ratio is (1+√5) : 2
so if 100 is the width, let the length be x
x/100 = (1+√5)/2
2x = 100 + 100√5
x = 50 + 50√5 or appr. 161.80
(The golden ratio is 1.618034 appr.
notice that our answer is 100 times that value)
To find the length of the unknown side of a golden rectangle, we need to understand the concept of the golden ratio. A golden rectangle is a rectangle whose side lengths are in the golden ratio, which is approximately 1.618.
Let's assume the length of the unknown side is "x." We are given that one dimension is 100.
According to the golden ratio, the ratio of the longer side to the shorter side in a golden rectangle is equal to the golden ratio or approximately 1.618.
So, we can set up the following equation:
100/x = 1.618
To find the value of x, we can solve this equation by cross-multiplying:
100 * 1.618 = x
161.8 = x
Therefore, the length of the unknown side is approximately 161.8.
To find the length of the unknown side in a golden rectangle with one dimension given as 100, we can use the concept of the golden ratio. The golden ratio, denoted by the Greek letter φ (phi), is approximately 1.618. It is a mathematical constant that often appears in nature and has aesthetic properties.
A golden rectangle is a rectangle where the ratio of the longer side to the shorter side is equal to the golden ratio. In other words, if we let x represent the length of the unknown side, then:
100 / x = φ
To solve for x, we can rearrange the equation:
x = 100 / φ
Now, to find the value of φ, we can use its approximate value of 1.618. Plugging in this value into the equation, we get:
x = 100 / 1.618 ≈ 61.8
Therefore, the length of the unknown side in the golden rectangle is approximately 61.8 units.
Note: It's important to remember that the golden ratio is an irrational number and has an infinite decimal expansion. The value of 1.618 is an approximation. For more precise calculations, you can use the exact value of φ.