Question : Three numbers are in the ratio 2 : 3 : 4. If the sum of their squares is 1856, the numbers are:
Option 1: 8, 12, and 16
Option 2: 16, 24, and 32
Option 3: 12, 18, and 24
Option 4: None of the above.
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Correct Answer: 16, 24, and 32
Solution : Given: Three numbers are in the ratio 2 : 3 : 4 and the sum of their squares is 1856. Let the numbers be $2x, 3x,$ and $4x$. According to the question, (2$x$) 2 + (3$x$) 2 + (4$x$) 2 = 1856 ⇒ 4$x$ 2 + 9$x$ 2 + 16$x$ 2 = 1856 ⇒ 29$x$ 2 = 1856 ⇒ $x$ 2 = 64 $\therefore x$ = 8 So, the numbers are (8 × 2) = 16, (8 × 3) = 24, and (8 × 4) = 32. Hence, the correct answer is "16, 24, and 32".
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Question : The sum of three positive numbers is 18 and their product is 162. If the sum of two numbers is equal to the third number, then the sum of the squares of the numbers is:
Question : The sum of three positive numbers is 18 and their product is 162. If the sum of two numbers is equal to the third number, the sum of the squares of the numbers is:
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