Mean proportional/ third proportional/ continued proportion of 12 and 12
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Subject:
Geography -
Author:
dilly dally -
Created:
1 year ago
Answers 1
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Three numbers are in continued proportion, whose mean proportional is 12 and the sum of the remaining two numbers is 26, then find these numbers.
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Solution
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Step 1 : Assume the number and follow given instruction
Let the there numbers be a,b,c
As they are in continued proportion
b
2
=ac
Given that mean proportional is 12
∴b=12
So, 12
2
=ac
144=ac
c=
a
144
The sum of the remaining two numbers is 26
a+c=26
a+
a
144
=26
Step 2 : Simplify using factorization
On solving we get,
⇒a
2
+144−26a=0
⇒a
2
−18a−8a+144=0
⇒a(a−18)−8(a−18)=0
⇒(a−18)(a−8)=0
∴a = 18 or a = 8
c = 8 or c = 18
Hence , The numbers are 8,12,18 or 18,12,
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