In a model, a² − b² is cut and rearranged into a rectangle. If the rectangle has length 15 and breadth 7, which pair of values for a and b can be correct?

Correct answer: a = 11, b = 4

The correct answer is A: a = 11 and b = 4. The difference-of-squares identity gives a² − b² = (a + b)(a − b). Therefore the two rectangle sides are a + b and a − b. Using the given sides, a + b = 15 and a − b = 7. Add the equations: 2a = 22, so a = 11. Subtract them: 2b = 8, so b = 4. Check: 11 + 4 = 15 and 11 − 4 = 7. Option B uses the rectangle sides directly as a and b, but then a + b and a − b would not be 15 and 7. Option C gives a + b = 15 but a − b = 1. Option D gives a + b = 30 and a − b = 14. The safe method is to use half the sum and half the difference.