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ICSE Class 10 Answered

Find the two numbers whose mean proportional is 28 and the third prortional is 224
Asked by Vijayalakshmigowrish | 05 Jan, 2019, 08:01: PM
answered-by-expert Expert Answer
Let two numbers be a and b. if mean proportion of a and b is 28, then we have begin mathsize 12px style square root of a space b end root space equals space 28 space o r space a space b space equals space 784 end style
third proportion is 224 means, we need to find numbers such that a:b = b:c , hence b2 = 224  or begin mathsize 12px style b space equals space 4 square root of 14 end style
hence a is given by
 
begin mathsize 12px style a space equals space fraction numerator a b over denominator b end fraction space equals space fraction numerator 28 cross times 28 over denominator 4 square root of 14 end fraction equals 14 square root of 14 end style
If third proportion of a nd b is 224, then we need to find numbers such that a:b = b:c
 
hence c = b2 / a  begin mathsize 12px style equals space fraction numerator 224 over denominator 14 square root of 14 end fraction space equals space 8 over 7 square root of 14 end style
Answered by Thiyagarajan K | 06 Jan, 2019, 08:45: AM

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