Mathematics Question and Solution
Calculating R.
(5+R)² = (10-R)²+(5-R)²
25+10R+R² = 100-20R+R²+25-10R+R²
20R = 100-20R+R²
R²-40R+100 = 0
Therefore;
R ≠ 20+10√(3) units.
R = 20-10√(3) units.
R = 2.67949192431 units.
Calculating r.
(5-r)² = r²+a²
25-10r+r² = r²+a²
a = √(25-10r) units.
Therefore;
(5+r)² = (5-r)²+ (5+√(25-10r))²
25+10r+r² = 25-10r+r²+25+10√(25-10r)+25-10r
20r = 25+10√(25-10r)+25-10r
30r-50 = 10√(25-10r)
(3r-5)² = 25-10r
9r²-30r+25 = 25-10r
9r² = 20r
9r = 20
r = ⅑(20) units.
r = 2.22 units.
It implies;
r ÷ R is;
(20/9) ÷ (20-10√(3))
= ⅑(4+2√(3))
= 0.8293446239
In percentage (%)
= ⅑(4+2√(3))*100
= (200(2+√(3))/9)%
= 82.93446239042%
