If a : b = 2 : 3 and b : c = 2 : 3, then a : b : c =?
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Answer:
a : b = 2 : 3 and b : c = 2 : 3
Formula Used:
If a : b = x : y and b : c = y : z
Then, a : b : c = x : y : z
Calculation:
a : b = 2 : 3 ---(1)
b : c = 2 : 3 ---(2)
⇒ a : b : c = 4 : 6 : 9
Now, (3a2 + b2 + c2) : (a2 + 2b2 + c2)
⇒ (3 × 42 + 62 + 92) : (42 + 2 × 62 + 92)
⇒ (3 × 16 + 36 + 81) : (16 + 2 × 36 + 81)
⇒ (48 + 36 + 81) : (16 + 72 + 81)
⇒ 165 : 169
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