Question

If three numbers are in the ratio 3:2:5 such that the sum of their squares is 1,862, the middle number will be:

• A. 7
• B. 14
• C. 21
• D. 35

Answer 1

The Correct Option is B

The three numbers in the ratio =\(3:2:5\)
The sum of the squares is equal to=\(1862\).
Ratio of three numbers are =\(3x: 2x: 5x\)
\((3x)^{2} + (2x)^{2} + (5x)^{2} = 1862\)
\(9x^{2} + 4x^{2} + 25x^{2} = 1862\)
\(x^{2}= \frac{1862}{38}\)
\(x=\sqrt49=7\)
The middle number is =\(2\times7=14\)
The correct answer is (B): 14