If a, b and c are positive numbers such that (a2 + b2) : (b2 + c2) : (c2 + a2) = 34 : 61 : 45, then b - a : c - b : c - a = ______________.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 2 : 1 : 3
(a2 + b2) : (b2 + c2) : (c2 + a2) = 34 : 61 : 45
(a2 + b2) = 34 units
(b2 + c2) = 61 units
(c2 + a2) = 45 units
On adding each we get,
2( a2 + b2 + c2) = 140
a2 + b2 + c2 = 70
a2 = 70 - 61 = 9
a = 3
b2 = 70 - 45 = 25
b = 5
c2 = 70 - 34 = 36
c = 6
b - a : c - b : c - a = 6 - 3 : 6 - 5 : 6 - 3
= 2 : 1 : 3