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Three numbers are in the ratio 4 ∶ 5 ∶ 6. If the sum of their squares is 1925, then what are the numbers?
- A20, 25, 30
- B15, 20, 40
- C20, 35, 30
- D40, 20, 10
Answer not set
Discussion 1
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CCommunity
Let the three numbers be 4x, 5x and 6x.
The sum of their squares = 1925
⇒ (4x)2 + (5x)2 + (6x)2 = 1925
⇒ 16x2 + 25x2 + 36x2 = 1925
⇒ 77x2 = 1925
⇒ x2 = 1925/77 = 25
⇒ x = 5
The three numbers are 4x = 20, 5x = 25 and 6x = 30
Hence, the three numbers are 20, 25 and 30.
The sum of their squares = 1925
⇒ (4x)2 + (5x)2 + (6x)2 = 1925
⇒ 16x2 + 25x2 + 36x2 = 1925
⇒ 77x2 = 1925
⇒ x2 = 1925/77 = 25
⇒ x = 5
The three numbers are 4x = 20, 5x = 25 and 6x = 30
Hence, the three numbers are 20, 25 and 30.