Mathematics Question and Solution
Let 1 unit be the side length of the green square.
Therefore;
EN = ½ units.
a = (1+2x) units.
a is the diameter of the bigger circle.
b = ½(a)
b = ½(1+2x) units.
b is the radius of the bigger circle.
c = b-2x
c = ½(1+2x)-2x
c = ½(1-2x) units.
It implies;
(½(1+2x))² = (½)²+(½(1-2x))²
¼(1+4x+4x²) = ¼+¼(1-4x+4x²)
1+4x+4x² = 1+1-4x+4x²
8x = 1
x = ⅛ units.
Recall.
b = ½(1+2x)
And x = ⅛ units.
b = ½(1+2*⅛)
b = ½(1+¼)
b = ⅛(5) units.
b = 0.625 units.
Calculating ME.
ME = MS+SE
SE = 2x
And x = ⅛ units.
SE = 2*⅛
SE = ¼ units.
MS is the radius of the radius of the red big circle.
Calculating MS, let it be d.
d² = (½)²+(¼)²
d² = ¼+(1/16)
d = √(5/16)
d =¼√(5) units.
d is MS.
It implies;
ME = ¼+¼√(5)
ME = ¼(1+√(5)) units.
Therefore;
ME÷EN is;
¼(1+√(5))÷½
= ¼(1+√(5))*2
= ½(1+√(5))
