Square tiles form (x^2+14x+49). Which two equal strip areas must have been added?

Correct answer: (7x) and (7x)

The direct answer is A. A square with side x+7 has area (x+7)^2. Expanding it gives x^2+2(x)(7)+7^2=x^2+14x+49. In an area model, x^2 is the large square, 49 is the smaller square, and the middle term 14x is made from two congruent rectangles. Each rectangle has dimensions x and 7, so each has area 7x. Adding them gives 7x+7x=14x. A therefore describes the two equal strips correctly. B would give 28x, not 14x, so it is too large. C gives 98x and uses the wrong dimensions. D names the two square regions, not the two equal rectangular strips. A useful memory cue is that the middle term in (x+k)^2 is 2kx: it represents two equal kx rectangles in the tile model.