Mathematics Question and Solution
Calculating x, chord of the circle..
a² = 1 square units.
a = 1 unit.
a is the side length of the 3 inscribed equal squares.
b = 1+½(1)+y
b = (1.5+y) units.
c = 1+1
c = 2 units.
d² = 2²+0.5²
d² = 4+0.25
d = √(4.25) units.
d is r, the radius of the circle.
e² = (1.5+y)²+1²
e² = 3.25+3y+y²
e = √(3.25+3y+y²) units.
e is also r, radius of the circle.
Calculating y.
Equating d and e.
√(4.25)² = √(3.25+3y+y²)
4.25 = 3.25+3y+y²
y²+3y-1 = 0
(y+(3/2))² = 1+(3/2)²
(y+(3/2))² = (13/4)
y = -(3/2)±√(13/4)
y = -(3/2)±√(13/4)
It implies;
y = ½(√(13)-3) units.
Therefore, x, red length is:
x = 1+1+1+½(√(13)-3)+½(√(13)-3)
x = 3+√(13)-3
x = √(13) units.
Calculating r, radius of the circle.
r² = (½√(13))²+1²
r² = ¼(13)+1
r = √(¼(17))
r = ½√(17) units.
Area of the circle is;
πr²
= π*(½√(17))²
= ¼(17π) square units.
