Mathematics Question and Solution
Let the length of the two congruent rectangle be 1 unit.
Let the width be x.
Therefore;
1 ~ (1+x)
x ~ 1
Cross Multiply.
1/x = (x+1)/1
x²+x-1 = 0
(x+½)²=1+¼
x = -½±½√(5)
Therefore;
x ≠ -½(1+√(5)) units.
x = ½(√(5)-1) units.
Let alpha be y.
Therefore;
Tany = (1+x)/1
Tany = (1+x)
And x = ½(√(5)-1) unit.
Tany = ½(√(5)-1)+1
Tany = ½√(5)-½+1
Tany = ½√(5)+½
Tany = ½(1+√(5))
Therefore;
Tany = Tan alpha = Golden Ratio
