If the three numbers in the ratio 3 : 2 : 5 be such that

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 ?

Let the numbers be 3x, 2x and 5x.
According to the question,
(3x)² + (2x)² + (5x)² = 1862
⇒ 9x² + 4x² + 25x² = 1862
⇒ 38x² = 1862

⇒ x² =	1862	= 49 = 5 : 2
	38

∴ x = √49 = 7
∴ Number in the middle
= 2x = 14