The following figure contains three squares with areas of 100, 16 and 49 lying side by side as shown. By how much should the area of the middle square be reduced in order that the total length PQ of the resulting three squares is 19?

The side length of a square equals the square root of its area, so the initial side lengths are √100 = 10, √16 = 4 and √49 = 7 . Thus the current total length PQ = 10 + 4 + 7 = 21. To make PQ = 19 the middle square’s side must become 19 − (10 + 7) = 2, so its new area would be 2^2 = 4. The original middle area was 16, so the required reduction is 16 − 4 = 12. Therefore option 1 (12) is correct.