Mathematics Question and Solution
Calculating x/y.
Let 10 units be the side length of the ascribed square.
x+y = 10
y = (10-x) --- (1).
Let a be each of the 2 equal angles.
tana = x/(10-x) --- (2).
tan(2a) = 10/(10-x)
2tana/(1-tan²a) = 10/(10-x)
10-10tan²a = 20tana-2xtana --- (3).
Substituting (2) in (3).
10-10(x/(10-x))² = 20(x/(10-x))-2x(x/(10-x))
10(10-x)²-10x² = 20x(10-x)-2x²(10-x)
10(100-20x+x²)-10x² = 200x-20x²-20x²+2x³
1000-200x = 200x-40x²+2x³
2x³-40x²+400x-1000 = 0
x³-20x²+200x-500 = 0
It implies;
x = 3.104
And x+y = 10
y = 10-x
y = 10-3.104
y = 6.896
Therefore, x/y is;
3.104/6.896
= 3104/6896
= 194/431
= 0.45011600928
