Solve hw wh w for w if h 1 and w 0 This number is the go

Solve h/w = w/h + w for w if h = 1 and w > 0. This number is the golden ratio. If a rectangle is to have sides with lengths in the golden ratio, what is the height if the length (the longer side) is one unit? If a window is to be 5 ft wide, how high should it be, to the nearest tenth of a foot, to be a golden rectangle?

Solution

53) h/w =w/(h+w)

given h =1

1/w =w/(1+w)

1(1+w)=w*w

1+w=w²

w²-w-1=0

w=(-(-1)+((-1)²-4*1*(-1)))/2

w=(1+(1+4))/2

w=(1+5)/2

w=1.618

54)h/w =w/(h+w)

w =1

h/1 =1/(h+1)

h=1/(h+1)

h(h+1)=1

h²+h -1=0

h =(-1+(1²-4*(-1)))/2

h =(-1+5)/2

h=0.618

55)w =5

h/w =w/(h+w)

h/5 =5/(h+5)

h(h+5)=5*5

h²+5h -25=0

h =(-5+(5²-4*(-25)))/2

h=5(-1+5)/2

h =3.09

h=3.1 ft