Mathematics Question and Solution
Let the radius of the green inscribed quarter circle be x.
Let the radius of the blue inscribed quarter circle be y.
a² =2x²
a = √(2)x units.
b = (x+1) units.
c = (y+1) units.
x²+(x+1)² = (x+y)² --- (1)
(x+y)² = (x+1)²+(y+1)² --- (2)
Substituting (2) in (1).
x²+(x+1)² = (x+1)²+(y+1)²
x² = (y+1)²
y = x-1 --- (3).
Substituting (3) in (1) to get x.
x²+(x+1)² = (x+x-1)²
x²+(x+1)² = (2x-1)²
Therefore;
2x²+2x+1 = 4x²-4x+1
2x²-6x = 0
2x = 6
x = 3 units.
It implies;
y is;
y = x-1
y = 3-1
y = 2 units.
Rectangle Length is;
x+1
= 3+1 = 4 units.
Rectangle Width is;
x = 3 units.
Or
y+1
= 2+1 = 3 units.
Perimeter Rectangle is;
2(4+3)
= 14 units.
Area Rectangle is;
(3*4)
= 12 square units.
