If 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.Options15141613
Question
If 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.Options15141613
Solution
The problem can be solved in the following steps:
Step 1: Let's assume the three numbers are 3x, 2x, and 5x.
Step 2: According to the problem, the sum of the squares of these numbers is 1862. So, we can write the equation as (3x)^2 + (2x)^2 + (5x)^2 = 1862.
Step 3: Simplifying the equation, we get 9x^2 + 4x^2 + 25x^2 = 1862.
Step 4: Adding the terms on the left side, we get 38x^2 = 1862.
Step 5: Solving for x, we get x = sqrt(1862/38) = sqrt(49) = 7.
Step 6: The middle number is 2x, so substituting x = 7, we get 2*7 = 14.
So, the middle number is 14.
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