Two numbers are in the ratio 3: 4. The difference between their squares is 28.…
2025
Two numbers are in the ratio 3: 4. The difference between their squares is 28. Find the sum of the squares of these numbers?
- A.
96
- B.
121
- C.
100
- D.
140
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Correct answer: C
Let the two numbers be 3k and 4k (since their ratio is 3:4).
Compute the difference of squares: (4k)^2 - (3k)^2 = 16k^2 - 9k^2 = 7k^2.
Set this equal to 28: 7k^2 = 28, so k^2 = 4 and k = 2.
The numbers are 3k = 6 and 4k = 8. Their squares are 36 and 64.
Sum of squares: 36 + 64 = 100.