Sum of squares of three positive numbers is 608 and they are in the ratio 2 : 3 : 5. Then, find the numbers.
A) 6, 9,15 |
B) 8, 12, 20 |
C) 10, 15,25 |
D) 14, 21, 35 |
B) 8, 12, 20 |
Let the common multiple factor be x.
Hence the three numbers are 2x, 3x and 5x
The sum of the squares of the numbers.
=> \( 4x^{2} + 9x^{2} + 25x^{2} = 608 \)
=> \( 38x^{2}= 608 \)
=>\( x^{2} = \frac{608}{38} \)
= > \( x^{2} = 16 \)
x = 4
Three numbers,
2x = 2 X 4 = 8;
3x=3 X 4=12;
5x = 5 X 4 = 20.