Question

three number are in the ratio 2: 3: 4. if the sum of their squares is 1856, then the numbers are ?​

Answer 1

Answer:

The numbers are 16, 24 and 32.

Step-by-step explanation:

The ratio of the Numbers = 2 : 3 : 4

Sum of their squares = 1856

Let the numbers be as -

• 2x
• 3x
• 4x

⟹ (2x)² + (3x)² + (4x)² = 1856

⟹ 4x² + 9x² + 16x² = 1856

⟹ 29x² = 1856

⟹ x² = 1856/29

⟹ x² = 64

⟹ x = $\sqrt{64}$

⟹ x = 8

One Number =

⟹ 2x

⟹ 2(8)

⟹ 16 ......... [ One Number ]

Second Number =

⟹ 3x

⟹ 3(8)

⟹ 24 ........ [ Second Number ]

Third Number =

⟹ 4x

⟹ 4(8)

⟹ 32 ....... [ Third Number ]

$\therefore$ The numbers are 16, 24 and 32.

Answer 2

Answer:

16,24,32

Step-by-step explanation:

Let the numbers be 2x,3x,4x

Thus the sum of their square is 1856

therefore (2x)^2 + (3x)^2 + (4x)^2 = 1856

or,4x^2 + 9x^2 + 16x^2 = 1856

or, 29x^2 = 1856

or, x = sq.root of 1856 /29

or, x = sq.root of 64

or, x = 8

Thus the numbers are 2×8=16 ,3×8=24 ,4×8=32

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