If three numbers are in the ratio 3 : 2 : 5 such that the sum of their squares…
2024
If three numbers are in the ratio 3 : 2 : 5 such that the sum of their squares is equal to 1862, the middle number is equal to :
- A.
7
- B.
14
- C.
21
- D.
35
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Correct answer: B
Let the three numbers be 3x, 2x, and 5x, as they are in the ratio 3 : 2 : 5.
Sum of their squares: (3x)² + (2x)² + (5x)² = 9x² + 4x² + 25x² = 38x².
Given that the sum of squares is 1862, so 38x² = 1862.
Solving for x: x² = 1862 / 38 = 49, so x = 7.
The middle number is 2x = 2 × 7 = 14.
हिन्दी उत्तर: माना तीन संख्याएँ 3x, 2x और 5x हैं, क्योंकि वे 3 : 2 : 5 के अनुपात में हैं।
उनके वर्गों का योग: (3x)² + (2x)² + (5x)² = 9x² + 4x² + 25x² = 38x²।
दिया गया है कि वर्गों का योग 1862 है, इसलिए 38x² = 1862।
x के लिए हल करने पर: x² = 1862 / 38 = 49, इसलिए x = 7।
मध्य वाली संख्या 2x = 2 × 7 = 14 है।