1. Given one side of a golden rectangle is 3.7 inches, find the possible lengths of the other side. Notice that the other side can be either longer or shorter than 3.7 inches. Round your answers to the nearest tenth and useGreek Phi normal.=1.618.
let the other side be x
case 1:
x/3.7 = 1.618
x = = 5.9866
or 6.0 inches to the nearest tenth
case 2:
3.7/x = 1.618
x = 3.7/1.618 = 2.286.. or appr 2.3 inches
To find the possible lengths of the other side of a golden rectangle, you can use the golden ratio, represented by the Greek letter Phi (φ), which is approximately 1.618.
Given that one side of the golden rectangle is 3.7 inches, you can calculate the other side as follows:
1. To find the longer side: Multiply the given side length (3.7 inches) by Phi (1.618).
Longer side length = 3.7 inches × 1.618 ≈ 5.99 inches (rounded to the nearest tenth).
2. To find the shorter side: Divide the given side length (3.7 inches) by Phi (1.618).
Shorter side length = 3.7 inches ÷ 1.618 ≈ 2.28 inches (rounded to the nearest tenth).
Therefore, the possible lengths of the other side of the golden rectangle are approximately 2.3 inches (shorter side) and 6.0 inches (longer side), rounded to the nearest tenth.
To find the possible lengths of the other side of a golden rectangle, we can use the golden ratio, also known as phi (Φ), which is approximately 1.618.
The golden ratio states that the ratio of the longer side to the shorter side in a golden rectangle is equal to phi (Φ), which can be expressed as follows:
(longer side) / (shorter side) = Φ
In this case, we know that one side of the golden rectangle is 3.7 inches. Let's denote this as the shorter side (S).
Therefore, we can set up the following equation:
(longer side) / (3.7 inches) = Φ
Now, we can rearrange the equation to solve for the longer side (L):
longer side = Φ * 3.7 inches
Using the value of Φ as approximately 1.618, we can calculate the longer side:
longer side ≈ 1.618 * 3.7 inches
longer side ≈ 5.9866 inches
Rounding this value to the nearest tenth, the possible length of the longer side is 6.0 inches.
So, for a given side of a golden rectangle measuring 3.7 inches, the possible lengths of the other side are approximately 5.9 inches (shorter side) and 6.0 inches (longer side), rounded to the nearest tenth.
Note: The actual value of the longer side may differ due to rounding.