Question

If three numbers are in the ratio 3:2:5 such that the sum of their squares is 1,862, the middle number will be:

• A. 7
• B. 14
• C. 21
• D. 35

Answer 1

Answer: (B)

14

Answer 2

The three numbers in the ratio =$3:2:5$
The sum of the squares is equal to=$1862$.
Ratio of three numbers are =$3x: 2x: 5x$
$(3x)^{2} + (2x)^{2} + (5x)^{2} = 1862$
$9x^{2} + 4x^{2} + 25x^{2} = 1862$
$x^{2}= \frac{1862}{38}$
$x=\sqrt49=7$
The middle number is =$2\times7=14$
The correct answer is (B): 14