Question

A room is approximately shaped like a golden rectangle. It's length is 23 ft. What is the rooms width? Write your answer in simplified radical form and rounded to the nearest tenth of a foot. Note that the ratio of the length to the width of a golden rectangle is (1+ ^5):2

Answer 1

`W=(-23+23√(5))/(2)\ ft`

`W=14.2\ ft`

Explanation:

Let

L ----> the length of rectangle in ft

W ----> the width of rectangle in ft

we know that

`(L)/(W) =(1+√(5))/(2)` -----> equation A

`L=23\ ft`

substitute the value of L in the equation A

`(23)/(W) =(1+√(5))/(2)`

`W=(46)/(1+√(5))`

Simplify

`W=(46)/(1+√(5))((1-√(5))/(1-√(5)))`

`W=(46(1-√(5)))/(1-5)`

`W=(46-46√(5))/(-4)`

`W=(23-23√(5))/(-2)`

`W=(-23+23√(5))/(2)`

`W=14.2\ ft`