A car fits onto a golden rectangle with a length of 12 ft. What is the car's width? Write your answer in simplified radical form and rounded to the nearest tenth of a foot.

Verified Answer :

basically, it is when legnth is \(\frac{1+ \sqrt{5} }{2}\) the width

legnth=12
legnth= \(\frac{1+ \sqrt{5} }{2}\) times width

12= \(\frac{1+ \sqrt{5} }{2}\) times width
multiply both sides by 2
24= \(1+ \sqrt{5}\) times width
subtract 1
23=√5 times width
divide both sides by √5
23/(√5)=width
multiply by (√5)/(√5) to rationalize denomenator
\(\frac{23 \sqrt{5} }{5}\)=width

aprox 10.28 so 10.3 ft

w=\(\frac{23 \sqrt{5} }{5}\) ft or aprox 10.3ft