SSC CPO SI and ASI Model Paper 10

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Question : 126 of 200

Marks: +1, -0

If

a +b +c + =6√ 3

and

a^ 2 +b ^2 +c ^2 =36

, then a : b : c = ?

1 : 2 : 3
3 : 2 : 1
1 : 1 : 1
2 : 1 : 3

Solution:

(3)

a +b + c = 6√ 3

Squaring both sides,

a^2 + b^2 +c2 +2(ab+bc+ca) =108

⇒36 +2(ab+bc+ca) =108

⇒2(ab+bc+ca) =72

⇒(ab+bc+ca) =36

∵ (ab+bc+ca) = a^2 +b^2 +c^2

∴a = b = c

∴a : b : c = 1 : 1 : 1

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