Mathematics Question and Solution
(AC)² = 2a²
AC = √(2)a units.
b² = 3²+4²
b = 5 units.
c = √(16-a²) units.
d = a-c
d = (a-√(16-a²)) units.
Therefore, considering similar triangle ratios.
a/4 = d/3. And d is (a-√(16-a²)).
Therefore;
a/4 = (a-√(16-a²))/3
Cross Multiply.
3a = 4a-4√(16-a²)
4√(16-a²) = a
16(16-a²) = a²
256-16a² = a²
256 = 17a²
a² = 256/17
a = 16/√(17)
a = (16√(17))/17 units.
a = 3.88057000058 units
Where a is a side length of the square ABCD.
