If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares…
2023
If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares is 1862, the middle number will be
Answer: B. 14 — Solution: Let the three numbers be 3x, 2x and 5x. Write the equation for the sum of squares: (3x)^2 + (2x)^2 + (5x)^2 = 1862, which simplifies to 9x^2 + 4x^2…
- A.
15
- B.
14
- C.
16
- D.
20
Attempted by 166 students.
Show answer & explanation
Correct answer: B
Solution: Let the three numbers be 3x, 2x and 5x.
Write the equation for the sum of squares: (3x)^2 + (2x)^2 + (5x)^2 = 1862, which simplifies to 9x^2 + 4x^2 + 25x^2 = 38x^2 = 1862.
Solve for x^2: x^2 = 1862 ÷ 38 = 49.
Take the positive root x = 7 (numbers in the given ratio are taken positive).
Middle number = 2x = 2 × 7 = 14.
Loading lesson…