If, in a square of side a+b, the part with area a² is 49 and the part with area b² is 9, what is the area of the whole square?

Correct answer: 100

The direct answer is C: 100. The area a² is 49, so the positive side length a is √49=7. Similarly, b²=9 gives b=√9=3. The whole square has side a+b=7+3=10, so its area is 10²=100. The identity also confirms this: (a+b)²=a²+2ab+b²=49+2(7)(3)+9=49+42+9=100. Option A, 64, is 49+9 and forgets the two rectangular parts 2ab. Option B, 80, does not follow from the given square sides. Option D, 112, uses an incorrect cross-term calculation. In a geometric model, the whole square contains two known smaller squares plus two rectangles, so simply adding 49 and 9 is incomplete. Memory cue: first take square roots of the square areas, add the side lengths, then square the sum.