Mathematics Question and Solution
Calculating Inscribed Blue Rectangle Area.
a = 15+5
a = 20 units.
Let b be the length of the blue inscribed rectangle.
b² = 2(20)²-2(20)²cos(90-x)
b² = 800-800(cos90cosx+sin90sinx)
b² = 800-800sinx --- (1).
b² = 2(15)²-2(15)²cos(90+x)
b² = 450-450(cos90cosx-sin90sinx)
b² = 450-450(-sinx)
b² = 450+450sinx --- (2).
Equating (1) and (2).
800-800sinx = 450+450sinx
350 = 1250sinx
sinx = 7/25
x = 16.2602047083°
It implies;
c² = 15²+20²-2*15*20cos16.2602047083
c = 7 units.
c is the width of the inscribed blue rectangle.
d = 90+x
d = 90+16.2602047083
d = 106.2602047083°
e² = 2(15)²-2(15)²cos106.2602047083
e = 24 units.
e is the length of the inscribed blue rectangle.
Area Blue Inscribed Rectangle is;
c*e
= 7*24
= 168 square units.
