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If three numbers in the ratio 3 : 2 : 5 be such that the sum of the squares is equal to 1862, then which number is the middle one. 
  • a)
    13 
  • b)
    15 
  • c)
    16 
  • d)
    14 
Correct answer is option 'D'. Can you explain this answer?
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Given:
Three numbers are in the ratio 3 : 2 : 5
Sum of the squares of the numbers is 1862

Let the numbers be 3x, 2x, and 5x

Sum of the squares of the numbers:
(3x)^2 + (2x)^2 + (5x)^2 = 1862
9x^2 + 4x^2 + 25x^2 = 1862
38x^2 = 1862
x^2 = 1862 / 38
x^2 = 49
x = 7

Therefore, the numbers are:
3x = 3 * 7 = 21
2x = 2 * 7 = 14
5x = 5 * 7 = 35

Identifying the middle number:
The middle number is 14, which corresponds to 2x.

Therefore, the middle number is 14. Option 'D' is correct.
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If three numbers in the ratio 3 : 2 : 5 be such that the sum of the squares is equal to 1862, then which number is the middle one.a)13b)15c)16d)14Correct answer is option 'D'. Can you explain this answer?
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