Calculating Area Square.
Let x be the side length of the square.
a²+x² = 13²
a = √(169-x²) cm
b = x-a
b = (x-√(169-x²)) cm.
c² = 2x²
c = √(2)x
c is the diagonal of the square.
Calculating x², area of the square.
x² = 3(½(x)√(169-x²))
2x² = 3x√(169-x²)
2x = 3√(169-x²)
4x² = 9(169-x²)
4x²+9x² = 9*169
13x² = 9*169
x² = 9*13
x² = 117 cm²
Again, x² is the area of the square.
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