Question

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.

Answer 1

basically, it is when legnth is
`(1+ √(5) )/(2)` the width

legnth=12
legnth=
`(1+ √(5) )/(2)` times width

12=
`(1+ √(5) )/(2)` times width
multiply both sides by 2
24=
`1+ √(5)` times width
subtract 1
23=√5 times width
divide both sides by √5
23/(√5)=width
multiply by (√5)/(√5) to rationalize denomenator

`(23 √(5) )/(5)`=width

aprox 10.28 so 10.3 ft

w=
`(23 √(5) )/(5)` ft or aprox 10.3ft