A golden rectangle has a length of 10 cm. The ratio of its length to its width is (1 + sqrt 5)/2 what is the width of the rectangle in simplified radical form? I need to know the formula to solve other problems like this.

Answer 1

10/w = (1+√5)/2
w = 10*2/(1+√5) = 20(√5-1)/(5-1) = 5(√5-1) = 10 * (√5-1)/2

Answer 2

How did the 5 - 1 get on the denominator?

Answer 3

On step 2