If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares is 1862, the middle number will be?Options :7211435
Question
If three numbers in the ratio 3 : 2 : 5 be such that the sum of their squares is 1862, the middle number will be?
Options: 7 2 1 1 4 3 5
Solution
Sure, let's solve this step by step:
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Let's assume the three numbers are 3x, 2x and 5x.
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According to the problem, the sum of their squares is 1862. So, we can write the equation as (3x)^2 + (2x)^2 + (5x)^2 = 1862.
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Simplifying the equation, we get 9x^2 + 4x^2 + 25x^2 = 1862.
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Adding the like terms, we get 38x^2 = 1862.
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Solving for x^2, we get x^2 = 1862 / 38 = 49.
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Taking the square root of both sides, we get x = 7.
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The middle number is 2x, so substituting x = 7, we get 2*7 = 14.
So, the middle number is 14.
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