Question

39.The sum of the squares between three numbers
is 5000. The ratio between the firstand the second
number is 3:4 and that of second and third number
is 4:5. Find the difference between first and the
thirdnumber..​

Answer 1

Answer: 20

Step-by-step explanation:

let all three numbers be a , b and c.

=>Ratio of numbers a and b = a:b => 3:4

=>Ratio of numbers b and c = b:c =>4:5

From this , we found

=> a = 3 ,

=> b = 4 and,

=> c = 5

So,Ratio of numbers a , b and c = a:b:c =>3:4:5

Let numbers a , b and c => 3x , 4x and 5x

=>sum of squares of these numbers = 5000

So,

(3x)^2 + (4x)^2 + (5x)^2 = 5000

=> 9x^2 + 16x^2 + 25x^2 = 5000

=> 50x^2 = 5000

=> x^2 = 5000/50

=> x^2 = 100

=> x = root 100

=> x = 10

then, all three numbers are:-

a => 3x => 3 x 10 = 30

b => 4x => 4 x 10 = 40

c => 5x => 5 x 10 = 50

NOW , difference between first and third number

=> c - a = 50 - 30 = 20