Question 54

Three positive numbers are in the proportion 3 : 4 : 6. If the sum of their squares is 244, then what is the largest number?

Solution

Given,

Ratio of three numbers is 3:4:6 and the sum of squares of three numbers is 244

let the three numbers be 3x,4x and 6x

therefore, $${(3x)^2}$$ + $${(4x)^2}$$ + $${(6x)^2}$$ = 244

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

$${61}{x^2}$$ = 244

$${x^2}$$ = $$\frac{244}{61}$$

$${x^2}$$ = 4

x = 2

hence the largest number is $${6}\times{2}$$ = 12

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