Mathematics Question and Solution
a² = 12²+16²
a = 20 units.
a is BC.
12b+16b+20b = 12*16
48b = 12*16
b = 4 units.
b is the radius of the inscribed circle.
tanc = 12/16
c = atan(3/4)°
d = 16-4
d = 12 units.
e = 90-½(atan(3/4))
e = 71.5650511771°
f = ½(e)
f = 35.7825255885°
tan35.7825255885 = g/4
g = 2.8830368802 units
h = 12-g
h = 9.1169631198 units.
Therefore, Area DEB is;
0.5*9.1169631198²sin(atan(3/4)
= 24.9357049583 square units.
Or
j = 2g
j = 5.7660737604 units.
It is;
0.5*9.1169631198*5.7660737604sin71.5650511771
= 24.9357049581 square units.
