Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side of the inscribed square be x.
Calculating x.
(10√(29)-√(29)x)/(5sin(45+atan½)) = (√(2)x)/(sin(90-atan½-atan(2/5))
It implies;
3√(5)x = 16√(5) - ⅕(8√(5))x
23√(5)x = 80√(5)
x = 80/23 units.
Calculating Area Purple exactly.
It is;
Area triangle with height (80√(2)/23) units and base (30√(29)/23)sin(45+atan(2/5)) units - Area triangle with height and base (80/23) units respectively.
= ½*(80√(2)/23)*(30√(29)/23)sin(45+atan(2/5)) - ½(80/23)²
= (8400/529) - (3200/529)
= (5200/529) square units.
