Find three numbers in the ratio 2:3:5, the sum of whose squares is 608.

Solution:

Given, three numbers are in the ratio 2 : 3 : 5

The sum of their squares is 608.

We have to find the numbers.

Let the numbers be 2x, 3x and 5x.

According to the question,

(2x)² + (3x)² + (5x)² = 608

4x² + 9x² + 25x² = 608

38x² = 608

x² = 608/38

x² = 304/19

x² = 16

Taking square root,

√x² = √16

= √(4)²

So, x = 4

Now, 2x = 2(4) = 8

3x = 3(4) = 12

5x = 5(4) = 20

Therefore, the required numbers are 8, 12 and 20.

✦ Try This: Find three numbers in the ratio 1:2:3, the sum of whose squares is 126.

☛ Also Check: NCERT Solutions for Class 8 Maths

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NCERT Exemplar Class 8 Maths Chapter 3 Problem 130

Find three numbers in the ratio 2:3:5, the sum of whose squares is 608

Summary:

The three numbers in the ratio 2:3:5, the sum of whose squares is 60, is 8, 12 and 20.

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