Consider two positive numbers that have a ratio of 5:7. If the combined total of their squares equals 1184, determine the sum of these two numbers.
Let the numbers be ‘5x’ and ‘7x’ ATQ, (5x)2 + (7x)2 = 1184 Or, 25x2 + 49x2 = 1184 Or, 74x2 = 1184 Or, x2 = (1184/74) = 16 Or, x = 4 {Since, the numbers are positive} Therefore, sum of numbers = (5x + 7x) = 12x = 12 × 4 = 48
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