Mathematics Question and Solution
a² = 2²+b²
a = √(4+b²)
a is AB.
b is the height of the yellow inscribed triangle.
0.5*b*c = 6
bc = 12
c = 12/b units.
c is the base of the inscribed yellow triangle.
d² = b²+(12/b)²
d² = (b⁴+12)/b²
d = √(b⁴+12)/b units.
2 - √(4+b²)
b - e
Cross Multiply.
e = ½√(4+b²)b units.
e is BC.
f = ½(e)
f = ¼√(4+b²)b units.
¼√(4+b²)b - b
g - 2
Cross Multiply.
g = ½√(4+b²) units.
It implies;
Calculating b.
12+(2*b)+(½√(4+b²)*½√(4+b²)b) = ½√(4+b²)b*√(4+b²)
12+2b+¼(4+b²)b = ½(4+b²)b
12+2b = ½(4+b²)b-¼(4+b²)b
12+2b = ¼(4+b²)b
48+8b = 4b+b³
b³-4b-48 = 0
It implies;
b = 4 units.
a = √(4+b²)
And b = 4 units.
a = √(4+4²)
a = √(20)
a = 2√(5) units.
Again, a is AB.
e = ½√(4+b²)b
And b = 4 units.
e = ½√(4+4²)*4
e = 2√(20)
e = 4√(5) units.
Therefore, Area ABC is;
½*a*e
= ½*2√(5)*4√(5)
= 4√(25)
= 20 square units.
