Mathematics Question and Solution
Calculating Area Inscribed Square
Let x be the length of the ascribed rectangle.
a²+2² = x²
a = √(x²-4) units.
Calculating x.
2 ~ √(x²-4)
√(x²-4) ~ 1
Cross Multiply.
2 = x²-4
x² = 6
x = √(6) units.
Again, x is the length of the ascribed rectangle.
b²+x² = (1+2)²
b²+√(6)² = 3²
b² = 9-6
b = √(3) units.
b is the width of the ascribed rectangle.
Let y be the side width of the inscribed rectangle .
tanc = √(6)/√(3)
c = atan(√(6)/√(3))°
Calculating y.
cosc = y/1
cos(atan(√(6)/√(3))) = y
y = 0.57735026919 units.
y = ⅓√(3) units.
Again, y is the width of the inscribed rectangle.
Let z be the length of the inscribed rectangle.
sinc = d/1
sin(atan√(6)/√(3)) = d
d = 0.81649658093 units.
z = x-2d
z = √(6)-2(0.81649658093)
z = 0.81649658093 units.
Therefore, area inscribed red rectangle is;
yz
= 0.57735026919*0.81649658093
= 0.47140452079 square units.
= ⅓√(2) square units.
