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Select the correct answerIf the 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.Options16131514

Question

Select the correct answerIf the 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.Options16131514

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Solution

Let's solve this step by step:

  1. Let's assume the three numbers are 3x, 2x, and 5x.

  2. According to the problem, the sum of the squares of these numbers is equal to 1862. So, we can write the equation as (3x)^2 + (2x)^2 + (5x)^2 = 1862.

  3. Simplifying the equation, we get 9x^2 + 4x^2 + 25x^2 = 1862.

  4. Adding the like terms, we get 38x^2 = 1862.

  5. Solving for x, we divide both sides by 38, we get x^2 = 49.

  6. Taking the square root of both sides, we get x = 7.

  7. The middle number is 2x, so substituting x = 7, we get 2*7 = 14.

So, the middle number is 14.

This problem has been solved

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