Calculating Square Area X ÷ Yellow Area Y.
a² = 100
a = 10 units.
a is the side length of the inscribed blue square.
b²+c² = a²
b² = 100-c²
b = √(100-c²) units.
b is the base of the green inscribed triangle with area 24 square units and c is the height.
Calculating c.
½*bc = 24
√(100-c²)*c = 48
(100-c²)c² = 48²
c⁴-100c² = -48²
c⁴-100c²+(-50)² = -48²+(-50)²
(c²-50)² = 196
c² = 50±√(196)
c² = 50±14
It implies;
c = √(50-14)
Or
c = √(50+14)
c = 6 units.
Or
c = 8 units.
Notice.
It implies,
c = 8 units, the height of the green inscribed triangle.
c = b = 6 units, the base of the green inscribed triangle.
Let d be the side length of Square X.
There;
d = b+c
d = 6+8
d = 14 units.
Again, d be the side length of Square X.
Therefore, Square Area X is;
d²
= 14²
= 196 square units.
Calculating e, radius of the inscribed yellow circle.
½(10e)+½(6e)+½(8e) = ½(6*8)
5e+3e+4e = 24
12e = 24
e = 2 units.
Again, e is the radius of the inscribed yellow circle.
Therefore,
Yellow Area Y is;
πe²
= π(2)²
= 4π square units.
It then implies that,
Square Area X ÷ Yellow Area Y is;
196÷(4π)
= 49/π
We appreciate you contacting us. Our support will get back in touch with you soon!
Have a great day!
Please note that your query will be processed only if we find it relevant. Rest all requests will be ignored. If you need help with the website, please login to your dashboard and connect to support