Question

Three numbers are in the ratio 2:3:8. If the sum of their squares is 693, find the largest of the three numbers.

Answer 1

three numbers are in the ratio =2:3:8

let the common factor =x

so, 2x,3x,8x

sum of the square:

4x^2+9x^2+64x^2=693

77x^2=693

x^2=9

therefore three numbers are:

2x=2×9=18

3x=3×9=37

8x=8×9=72

18:37:72

Answer 2

The largest of the three numbers is 72.

Given: Three numbers are in the ratio 2: 3: 8. The sum of their squares is 693.

To Find: The largest of the three numbers.

Solution:

It is said that the three numbers are in the ratio = 2: 3: 8

let the constant factor of the ratio be 'x'.

so, the numbers are = 2x, 3x, 8x

It is said that the sum of the squares is equal to 693. So, we can frame an equation that says;

     4x² + 9x² + 64x² = 693

  ⇒ 77x² = 693

  ⇒ x² = 693 / 77

  ⇒ x²  =  9

  ⇒  x  =  3

therefore three numbers are:

⇒ 2x = 2 × 9 = 18

⇒ 3x = 3 × 9 = 37

⇒ 8x = 8 × 9 = 72

Hence, the largest of the three numbers is 72.

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