Mathematics Question and Solution
Let the two equal inscribed right-angled triangle side lengths be a each.
Calculating a.
0.5a² = 50
a² = 100
a = 10 units.
a is EU.
Notice!
Arc TU = Arc US.
Let b be the radius of the ascribed quarter circle.
Calculating b.
sin(0.5*45) = (0.5*10)/b
sin22.5 = 5/b
b = 5/sin(22.5)
b = 13.0656296488 units.
Therefore, ascribed quarter circle perimeter is;
¼*2πb+2b
= 0.25*2*π*13.0656296488+2*13.0656296488
= 46.6547023572 units.
