Mathematics Question and Solution
Calculating Square Area.
Let x be the side length of the square.
a = 4+2
a = 6 cm.
b²+x² = 6²
b² = 36-x²
b = √(36-x²) units.
c = ½(4)
c = 2 units.
Calculating x² (Area of the square).
6 ~ x
√(36-x²) ~ 2
Cross Multiply.
12 = x√(36-x²)
144 = x²(36-x²)
x⁴-36x²+44 = 0
Let x² = p.
Therefore;
p²-36p+144 = 0
(p-18)² = -144+(-18)²
(p-18)² = -144+324
(p-18)² = 180
p-18 = ±√(180)
p = 18±6√(5)
It implies;
p = 18-6√(5)
Or
p = 18+6√(5)
And p = x²
Therefore;
x² ≠ 18-6√(5) square units.
x² = 18+6√(5) square units.
x² = 31.416407865 square units.
Again, x² is the area of the square.
