Mathematics Question and Solution
Calculating x, the side length of the ascribed square.
a²+x² = 8²
a = √(64-x²) units.
b²+x² = 10²
b = √(100-x²) units.
It implies;.
c = (x-√(64-x²)) units.
d = (x-√(100-x²)) units.
Therefore;
⅛(√(64-x²)) = ⅙(x-√(100-x²))
4(x-√(100-x²)) = 3√(64-x²)
4x-4√(100-x²) = 3√(64-x²)
16x²-32x√(100-x²)+1600-16x² = 576-9x²
9x²+1024 = 32x√(100-x²)
81x⁴+18432x²+1048576 = 102400x²-1024x⁴
1105x⁴-83968x²+1048576 = 0
Therefore;
x² = 60.2353
Or
x² = 15.7538
It implies;
x ≠ √(60.2353) units.
x = √(15.7538) units.
x = 3.96910569272 units.
x is the side length of the square.
