Question
Three positive numbers are in the ratio 2:3:4. If the sum
of their squares is 2349, what is the average of the two largest numbers?Solution
ATQ,
Let the three numbers be 2x, 3x and 4x, respectively.
ATQ;
(2x)² + (3x)² + (4x)² = 2349
Or, 4x² + 9x² + 16x² = 2349
Or, 29x² = 2349
Or, x² = 81
So, x = 9 (Since, numbers are positive therefore we can discard the negative root)
So, required average = {(3 X 9) + (4 X 9) } ÷ 2 = (63/2) = 31.5
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