Two numbers are in the ratio 3: 4. The difference between their squares is 28.…

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.