Mathematics Question and Solution
Calculating r, radius of the circle.
a² = 4
a= 2 cm.
a is the side length of the small square.
b = (r-2) cm.
It implies;
r² = 4²+(r-2)²
r² = 16+r²-4r+4
4r = 20
r = 5 cm.
Again, r is the radius of the circle.
Calculating x, side length of the big square.
c = (x-5) cm.
It implies;
5² = (x-5)²+√(21)²
25-21 = x²-10x+25
x²-10x+21 = 0
Resolving the above quadratic equation via factorization approach to get x.
x²-7x-3x+21 = 0
x(x-7)-3(x-7) = 0
(x-3)(x-7) = 0
Therefore;
x ≠ 3 cm.
x = 7 cm.
It implies;
x² (area of the big square) is;
7²
= 7*7
= 49 cm²
