Mathematics Question and Solution
5² = x²+a²
a = √(25-x²) units.
b = x-a
b = (x-√(25-x²)) units.
c² = 4²-x²
c = √(16-x²) units.
Calculating x, the ascribed square side length.
Observing similar plane shape (right-angled) side length ratios.
3 - 4
(x-√(25-x²)) - √(16-x²)
Cross Multiply.
3√(16-x²) = 4(x-√(25-x²))
3√(16-x²) = 4x-4√(25-x²)
3²(16-x²) = (4x-4√(25-x²))²
144-9x² = 16x²-32x√(25-x²)+16(25-x²)
144-9x² = 16x²-32x√(25-x²)+400-16x²
144-9x² = 400-32x√(25-x²)
32x√(25-x²) = 256+9x²
(32x)²(25-x²) = (256+9x²)²
25600x²-1024x⁴ = 65536+4608x²+81x⁴
1105x⁴-20992x²+65536 = 0
It implies;
x = 16√(17)/17 units.
x = 3.8805700006 units.
Again, x is the side length of the ascribed square.
