Mathematics Question and Solution
Calculating Square Area.
Let x be the side length of the square.
a = 7+6
a = 13 units.
6²+b² = x²
b = √(x²-36) units.
It implies;
sinc = x/a
sinc = x/13 --- (1).
sinc = b/x
sinc = √(x²-36)/x --- (2).
Equating (1) and (2).
x/13 = √(x²-36)/x
Cross Multiply.
x² = 13√(x²-36)
Notice.
x² is the area of the square.
Calculating x².
It implies;
(x²)² = 13²(x²-36)
x⁴ = 169x²-6084
x⁴-169x²+6084 = 0
(x²-½(169))² = -6084+(-½(169))²
(x²-½(169))² = 1056.25
x² = 84.5±√(1056.25)
x² = 84.5±32.5
x² ≠ 84.5-32.5
x² = 84.5+32.5
x² = 117 square units.
Again, x² is the area of the square.
