Question

Three positive numbers are in ratio 1:2:1:3:1:4.find the no. If the sum of their squares is 224

Answer 1

Sol:
Ratio of three positive numbers = 1/2 : 1/3 : 1/4
LCM of 2, 3 and 4 = 12
1/2 : 1/3 : 1/4 = 6 : 4 : 3
Let the numbers be 6x, 4x and 3x.
⇒ (6x)2 + (4x)2 + (3x)2 = 244
⇒ 36x2 + 16x2 + 9x2 = 244
⇒ 61x2 = 244
⇒ x2 = 4
⇒ x = ±2
The numbers are positive.
Therefore, three numbers are (6 x 2), (4 x 2), (3 x 2) i.e. 12, 8 and 6.
I hope its like this.... the

Answer 2

Answer:

12 , 8 and 6

Step-by-step explanation:

We are given that the ratio of three positive numbers are  1/2 : 1/3 : 1/4

LCM of 2, 3 and 4 = 12

So,$\frac{1}{2} : \frac{1}{3} : \frac{1}{4} = 6 : 4 : 3$

Let the numbers be 6x, 4x and 3x.

$(6x)^2+(4x)^2+ (3x)^2= 244$

$36x^2+ 16x^2+ 9x^2= 244$

$61x^2= 244$

$x^2= 4$

$x=2$

6x = 12

4x=8

3x = 6

Therefore, three numbers are 12 , 8 and 6