Mathematics Question and Solution
Calculating Length AB.
Notice.
The ascribed plane shape is a square.
Let x be the radius of the inscribed half circle.
Let y be the radius of the inscribed circle.
a² = 2(12)²
a = 12√(2) cm.
b = a-12
b = (12√(2)-12) cm.
Calculating x.
It implies;
x = b
x = (12√(2)-12) cm.
x = 4.97056274848 cm.
Again, x is the radius of the inscribed half circle.
c = 12-x
c = 12-(12√(2)-12)
c = (24-12√(2))
c = 7.02943725152 cm.
Calculating y.
d = ½(12√(2))-y
d = (6√(2)-y) cm.
It implies;
2y² = (6√(2)-y)²
2y² = 72-12√(2)y+y²
y²+12√(y)-72 = 0
Therefore;
y ≠ -20.485
y = 3.515 cm.
Again, y is the radius of the inscribed circle.
e = c-y
e = 7.02943725152-3.515
e = 3.51443725152 cm.
f = 12-y
f = 12-3.515
f = 8.485 cm.
It implies, length AB is;
(AB)² = e²+f²
AB = √(3.51443725152²+8.485²)
AB = 9.18403474486 cm.
