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Question

# Find three numbers which are in the ratio 2:3:5 and the sum of whose squares is 608

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Solution

## What is ratio? A ratio is that you get when you eliminate all common factors. Eg : 6/3 - 3 is common Factor. So, cancelling 3, you get 2/1 , so ratio is 2:1. Similarly, you can write, 6/3 = 2x/3x , where x is the common factor, in this case , x= 3. Which means, when you multiply a ratio by its common Factor again, you get the actual number back. So, in our question, We have 2:3:5 . Here, all common factors are cancelled .To get the number back, multiply each term by its common factor. Let common factor be x. So, the ratio becomes 2x:3x:5x, and the numbers are 2x, 3x and 4x respectively. Given, sum of squares of numbers is 608. So, (2x)²+(3x)²+(5x)²=608 ​​​​​So ;4 x²+9 x²+25 x² = 608 38x²= 608 x² = 608/38 = 16 x = ✓16 = 4. hence numbers are 2x, 3x and 5x 2x = 2* 4 = 8 3x = 3*4 = 12 5x = 5*4 = 20 So, numbers are 8, 12 and 20. Their ratio is 8:12:20 = 2:3:5

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