Question

three numbers are in the ratio of 2:3:5 . The sum of their squares is 608. find the numbers.

Answer 1

GIVEN

Three Numbers are in ratio of 2:3:5

The sum of their squares is 608

TO FIND

Those Numbers

SOLUTION

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

According to the question,

(2x)^2 + (3x)^2 + (5x)^2 = 608

=> 4x^2 + 9x^2 + 25x^2 = 608

=> 38x^2 = 608

=> x^2 = 608/38

=> x^2 = 16

=> x = 4

If x = 4 , the numbers are

2x = 8

3x = 12

5x = 20

Hence the numbers are 8,12 and 20 (Ans)

Answer 2

Answer :-

8, 12, 20 are the required numbers.

Explanation :-

Given :-

Ratio of three numbers = 2 : 3 : 5

Sum of their squares = 608

To find :-

Three numbers

Solution :-

Ratio of three numbers = 2 : 3 : 5

Let the three numbers be 2x, 3x, 5x

Square of 2x = (2x)² = 4x²

Square of 3x = (3x)² = 9x²

Square of 5x = (5x)² = 25x²

Sum of their squares = 608

⇒ 4x² + 9x² + 25x² = 608

⇒ 38x² = 608

⇒ x² = 608/38

⇒ x² = 16

⇒ x = √16

⇒ x = 4

• One of the number = 2x = 2(4) = 8

• Another number = 3x = 3(4) = 12

• Third number = 5x = 5(4) = 20

Therefore 8, 12, 20 are the required numbers.

Verification :-

4x² + 9x² + 25x² = 608

⇒ (8)² + (12)² + (20)² = 608

⇒ 64 + 144 + 400 = 608

⇒ 608 = 608