If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares…

2023

If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares is 1862, the middle number will be

  1. A.

    15

  2. B.

    14

  3. C.

    16

  4. D.

    20

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Show answer & explanation

Correct answer: B

Solution: Let the three numbers be 3x, 2x and 5x.

  1. Write the equation for the sum of squares: (3x)^2 + (2x)^2 + (5x)^2 = 1862, which simplifies to 9x^2 + 4x^2 + 25x^2 = 38x^2 = 1862.

  2. Solve for x^2: x^2 = 1862 ÷ 38 = 49.

  3. Take the positive root x = 7 (numbers in the given ratio are taken positive).

  4. Middle number = 2x = 2 × 7 = 14.

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