A golden rectangle has a diagonal measuring 12units.What are the measures of the sides of the rectangle

Question

Ratios

 

Answer 1

The dimension of a Golden Rectangle is 

1 : (1 +√5)/2

Use these values to calculate the hypotenuse (diagonal)

Use that value to create proportion with the diagonal of 12 units.

Answer 2

For a golden rectangle (side b )/(side a )= 1.618 where b is longer side of rectangle

 

Diagonal = sqr root ( a² +b²)  = 12

             (a2 +b2) =144

 

a² +( 1.618)² a² = 144

 

a² (1+ 2.618)   = 144

 

a² x (3.618)= 144

 

a= 12/ √3.618 and b= ax 1.618 

 

 

Answer 3

The ratio, as Mark said, of the sides of the

Golden Rectangle are1 : (1 +√5)/2 or  1:1.618  ...

 

Using Pythagorean Theorem

1 side length = x

other side = 1.618x

hypotenuse = 12

 

x² + (1.618x)² = 12²