Mathematics Question and Solution
Calculating x.
Let a be the side length of the square.
b² = 2a²
b = √(2)a units.
c = ½(b)
c = ½√(2)a units.
a ~ 1
0.5 ~ d
Cross Multiply.
d = 1/(2a) units.
Calculating a.
c+d = a
½√(2)a+(1/(2a)) = a
√(2)a²+1 = 2a²
(2-√(2))a² = 1
a = √(1/(2-√(2)))
a = 1.30656296488 units.
Again, a is the side length of the square.
Recall.
d = 1/(2a) units.
And a = 1.30656296488 units.
d = 1/2(1.30656296488)
d = 0.38268343236 units.
e² = d²+d²
e² = 2(0.38268343236)²
e = √(2(0.38268343236)²)
e = 0.54119610014 units.
Therefore, length x is;
x² = e²+a²
x² = 0.54119610014²+1.30656296488²
x = √(0.54119610014²+1.30656296488²)
x = 1.41421356237 units.
x = √(2) units.
