solving equations by algebratic method請列式(other question)

for the original rectangle

width = 1cm
length = x cm greater than 1 cm

length to width ratio = x / 1 = x

for the remaining rectangle

width = x - 1 cm smaller than 1 cm
length = 1 cm

length to width ratio = 1 / (x - 1)

Under the similarity definition, they should have the same ratio. Hence,

x = 1 / (x - 1)
iff
(x ^ 2) - x - 1 = 0
iff
[2x - 1 - sqrt(5)] * [2x - 1 + sqrt(5)] = 0

however, x > 1

As a result, x = [1 + sqrt(5)] / 2