Mathematics Question and Solution
Calculating Area Blue.
Let r be the radius of the biggest circle, also the side length of the blue square.
a = 4+9
a = 13 units.
b = (r-4) units.
c = (r-9) units.
d = (r+9) units.
e = (r-9) units.
It implies;
f²+(r-9)² = (r+9)²
f² = r²+18r+81-(r²-18r+81)
f² = 36r
f = √(36r)
f = 6√(r) units.
g = 2r-4-9
g = (2r-13) units.
13² = (2r-13)²+ h²
h² = 169-(4r²-52r+169)
h² = 52r-4r²
h = √(52r-4r²) units.
j = (r+4) units.
(r+4)² = (r-4)²+k²
r²+8r+16 = r²-8r+16+k²
k² = 16r
k = √(16)r
k = 4√(r) units.
Calculating r.
f = h+k
6√(r) = √(52r-4r²)+4√(r)
6√(r)-4√(r) = √(52r-4r²)
(6√(r)-4√(r))² = 52r-4r²
36r-48r+16r = 52r-4r²
4r = 52r-4r²
4r² = 52r-4r
4r² = 48r
It implies;
r ≠ 0
4r = 48
r = 12 units.
Therefore, area of the inscribed square is;
r²
= 12²
= 144 square units.
