Length of Golden Rectangle given Diagonal Solution

STEP 0: Pre-Calculation Summary
Formula Used
Length of Golden Rectangle = [phi]/(sqrt(1+[phi]^2))*Diagonal of Golden Rectangle
l = [phi]/(sqrt(1+[phi]^2))*d
This formula uses 1 Constants, 1 Functions, 2 Variables
Constants Used
[phi] - Golden ratio Value Taken As 1.61803398874989484820458683436563811
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Length of Golden Rectangle - (Measured in Meter) - The Length of Golden Rectangle is the length of the longest edge of the Golden Rectangle.
Diagonal of Golden Rectangle - (Measured in Meter) - The Diagonal of Golden Rectangle is the distance between any pair of opposite vertices of Golden Rectangle.
STEP 1: Convert Input(s) to Base Unit
Diagonal of Golden Rectangle: 12 Meter --> 12 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
l = [phi]/(sqrt(1+[phi]^2))*d --> [phi]/(sqrt(1+[phi]^2))*12
Evaluating ... ...
l = 10.2078097002245
STEP 3: Convert Result to Output's Unit
10.2078097002245 Meter --> No Conversion Required
FINAL ANSWER
10.2078097002245 10.20781 Meter <-- Length of Golden Rectangle
(Calculation completed in 00.004 seconds)

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Length of Golden Rectangle Calculators

Length of Golden Rectangle given Diagonal
​ LaTeX ​ Go Length of Golden Rectangle = [phi]/(sqrt(1+[phi]^2))*Diagonal of Golden Rectangle
Length of Golden Rectangle given Perimeter
​ LaTeX ​ Go Length of Golden Rectangle = [phi]/(2*(1+[phi]))*Perimeter of Golden Rectangle
Length of Golden Rectangle given Area
​ LaTeX ​ Go Length of Golden Rectangle = sqrt([phi]*Area of Golden Rectangle)
Length of Golden Rectangle
​ LaTeX ​ Go Length of Golden Rectangle = [phi]*Breadth of Golden Rectangle

Length of Golden Rectangle given Diagonal Formula

​LaTeX ​Go
Length of Golden Rectangle = [phi]/(sqrt(1+[phi]^2))*Diagonal of Golden Rectangle
l = [phi]/(sqrt(1+[phi]^2))*d

What is a Golden Rectangle?

In geometry, a golden rectangle is a rectangle whose side lengths are in the golden ratio, 1:1+sqrt(5)/2 which is 1:phi is approximately 1.618. Golden rectangles exhibit a special form of self-similarity: All rectangles created by adding or removing a square are Golden rectangles as well. A distinctive feature of this shape is that when a square section is added—or removed—the product is another golden rectangle, having the same aspect ratio as the first. Square addition or removal can be repeated infinitely, in which case corresponding corners of the squares form an infinite sequence of points on the golden spiral, the unique logarithmic spiral with this property. Diagonal lines drawn between the first two orders of embedded golden rectangles will define the intersection point of the diagonals of all the embedded golden rectangles; Clifford A. Pickover referred to this point as "the Eye of God"

How to Calculate Length of Golden Rectangle given Diagonal?

Length of Golden Rectangle given Diagonal calculator uses Length of Golden Rectangle = [phi]/(sqrt(1+[phi]^2))*Diagonal of Golden Rectangle to calculate the Length of Golden Rectangle, The Length of Golden Rectangle given Diagonal formula is defined as the length of the longest edge of the Golden Rectangle and calculated using the diagonal of the Golden Rectangle. Length of Golden Rectangle is denoted by l symbol.

How to calculate Length of Golden Rectangle given Diagonal using this online calculator? To use this online calculator for Length of Golden Rectangle given Diagonal, enter Diagonal of Golden Rectangle (d) and hit the calculate button. Here is how the Length of Golden Rectangle given Diagonal calculation can be explained with given input values -> 10.20781 = [phi]/(sqrt(1+[phi]^2))*12.

FAQ

What is Length of Golden Rectangle given Diagonal?
The Length of Golden Rectangle given Diagonal formula is defined as the length of the longest edge of the Golden Rectangle and calculated using the diagonal of the Golden Rectangle and is represented as l = [phi]/(sqrt(1+[phi]^2))*d or Length of Golden Rectangle = [phi]/(sqrt(1+[phi]^2))*Diagonal of Golden Rectangle. The Diagonal of Golden Rectangle is the distance between any pair of opposite vertices of Golden Rectangle.
How to calculate Length of Golden Rectangle given Diagonal?
The Length of Golden Rectangle given Diagonal formula is defined as the length of the longest edge of the Golden Rectangle and calculated using the diagonal of the Golden Rectangle is calculated using Length of Golden Rectangle = [phi]/(sqrt(1+[phi]^2))*Diagonal of Golden Rectangle. To calculate Length of Golden Rectangle given Diagonal, you need Diagonal of Golden Rectangle (d). With our tool, you need to enter the respective value for Diagonal of Golden Rectangle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Length of Golden Rectangle?
In this formula, Length of Golden Rectangle uses Diagonal of Golden Rectangle. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Length of Golden Rectangle = [phi]*Breadth of Golden Rectangle
  • Length of Golden Rectangle = [phi]/(2*(1+[phi]))*Perimeter of Golden Rectangle
  • Length of Golden Rectangle = sqrt([phi]*Area of Golden Rectangle)
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