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three numbers are in the ratio 2:3:5 and the sum of their
squares is 152, what will be their sum ?
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Answer Posted / jerry
ratio of three numbers is 2:3:5. First add the numbers (as
can be done with any ratio) 2+3+5=10, therefore: let y be
each ratio.
y1/10=x^2/152
y1*(152)/10 = x^2
y1*(15.2)=x^2, the same for the other three numbers in ratio
Now substitute each ratio number:
2*(15.2)=x1^2=30.4, x=(30.4)^1/2 = 5.5136195
to five sigficant digits, now the next numbers in ratio
3*(15.2)=x2=(45.6)^1/2
5*(15.2)=x3=(76)^1/2
X1=5.5136195
X2=6.7527772
X3=8.7177978
What will their sum be?:
X1+X2+X3=5.5136195+6.7527772+8.7177978= 20.9841945
X1^2+X2^2+X3^2=152
also note sum of squares:
(5.5136195)^2+(6.7527772)^2+(8.7177978)^2=152
Also note:
30.4+45.6+76=152 because these are the squares of the above
sum of squares.ex. 30.4 =(5.5136195)^2
also note:
30.4:45.6:76 is the ratio of the X's above
then division by 30.4:
1:1.5:2.5
then multiply by 2:
2:3:5 =>have check answer as requested
| Is This Answer Correct ? | 6 Yes | 3 No |
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