Mathematics Question and Solution
Calculating b/a.
Let x be the side length of the square.
Therefore;
a+b = x
c² = 15²+8²
c² = 225+64
c = √(289)
c = 17 units.
d²+x² = 17²
d = √(289-x²) units.
e = x-d
e = (x-√(289-x²)) units.
b²+x² = 15²
b = √(225-x²) units.
Recall.
a+b = x
And b = √(225-x²) units.
a = (x-√(225-x²)) units.
cosy = x/15 --- (2).
cosy = (x-√(225-x²))/8 --- (3).
Equating (2) and (3).
x/15 = (x-√(225-x²))/8
8x = 15(x-√(225-x²))
8x = 15x-15√(225-x²)
15√(225-x²) = 7x
225(225-x²) = 49x²
50625-225x² = 49x²
50625 = 274x²
x² = 50625/274
x = √(184.762773723)
x = 13.5927470999 units.
Again, x is the side length of the square.
Recall.
b = √(225-x²)
And x = 13.5927470999 units.
b = √(225-13.5927470999²)
b = 6.34328198003 units.
Recall Again.
a+b = x
And b = 6.34328198003 units, x = 13.5927470999 units.
Therefore;
a = x-b
a = 13.5927470999-6.34328198003
a = 7.24946511987 units.
Therefore, b/a is;
6.34328198003/7.24946511987
= 0.875
= 875/1000
= 35/40
= 7/8
