rect 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.Options16131415

The problem is asking for the middle number in the ratio 3:2:5, given that the sum of the squares of these numbers is equal to 1862.

Here are the steps to solve this problem:

1. Let's denote the three numbers as 3x, 2x, and 5x. These numbers are in the ratio 3:2:5.

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 gives 9x^2 + 4x^2 + 25x^2 = 1862, which simplifies further to 38x^2 = 1862.

4. Solving for x, we get x^2 = 1862 / 38, which simplifies to x^2 = 49. Therefore, x = sqrt(49) = 7.

5. The middle number in the ratio 3:2:5 is 2x, so substituting x = 7, we get 2*7 = 14.

So, the middle number is 14.