Mathematics Question and Solution
Let the side length of the red square be a units.
b²+3² = a²
b = √(a²-9) units.
c²+6² = a²
c = √(a²-36) units.
Observing similar plane shape (right-angled) side length ratios.
√(a²-9) - 6
3 - √(a²-36)
Cross Multiply.
√(a²-36)√(a²-9) = 18
(a²-36)(a²-9) = 18²
(a²-36)(a²-9) = 324
a⁴-45a²+324 = 324
a⁴ = 45a²
a² = 45 square units.
Where a² is the red square area.
Notice!
a = 3√(5) units is the side length of the red square.
