Mathematics Question and Solution
Calculating the area of the quarter circle.
Let r be it's radius.
Let a be the 3 equal lengths each.
b = r-a-a-a
b = (r-3a) units.
c = a+a+a
c = 3a units.
d = r+a+a+a
d = (r+3a) units.
It implies;
(r+3a)(r-3a) = 13²
r²-9a² = 169
r² = 169+9a² --- (1).
Therefore;
(r+2a)(r-2a) = 17²
r²-4a² = 289
r² = 289+4a² --- (2).
(r+a)(r-a) = 19²
r²-a² = 361
r² = 361+a² --- (3).
Equating (1) and (2).
169+9a² = 289+4a²
5a² = 120
a² = 24
a = √(24)
a = 2√(6) units.
Calculating r.
Substituting a in (3).
r² = 361+a²
And a = 2√(6) units.
r² = 361+(2√(6))²
r² = 361+24
r = √(385) units.
Again, r is the radius of the quarter circle.
Therefore, area quarter circle is;
¼(πr²)
= ¼*π√(385)²
= ¼(385π) square units.
= 96.25π square units.
