Mathematics Question and Solution
Let the ascribed square side be be 4 units.
Area ascribed square is;
4²
= 16 square units.
Calculating the inscribed red rectangle.
It implies;
a² = 2²+1²
a = √(5) units.
b² = 1²+0.5²
b = √(5/4)
b = ½√(5) units.
Observing similar plane shape (right-angled) side length ratios.
2 - ½√(5)
c - ½
Cross Multiply.
√(5)c = 2
c = ⅕(2√(5)) units.
d = c+a
d= ⅕(2√(5))+√(5)
d = ⅕(7√(5)) units.
Therefore, area inscribed red rectangle is;
a*d
= √(5)*⅕(7√(5))
= 7 square units.
It implies;
Shaded fraction of the large square is;
7/16
= 0.4375
