Question 175758
If the width (shorter length) of a golden rectangle is 1, then the length is {{{(1 + sqrt(5))/2}}}.  So for this situation, if the width is {{{x}}} and 36 is the length,


{{{(x (1 + sqrt(5)))/2 = 36}}}


Solve for x:


{{{x = (36 * 2)/(1 + sqrt(5)) = 72/(1 + sqrt(5))}}}


Now rationalize the denominator using the conjugate of {{{(1 + sqrt(5))}}}, namely {{{1 - sqrt(5))}}}, so:


{{{(72/(1 + sqrt(5)))((1 - sqrt(5))/(1 - sqrt(5)))=(72 - 72(sqrt(5)))/(-4)=18*sqrt(5) - 18}}}


That's the exact answer.  If you need a numerical approximation, use your calculator.  However, round your answer to the nearest inch because you should never, unless specifically instructed otherwise, express an answer to a calculation involving measurements to a greater precision than the least precise given measurement.  In this case, the length was expressed to the inch, so your answer must be to the nearest inch.