A tile model forms the rectangle x² + 9x + 20. Which side lengths are correct?

Correct answer: x + 4 and x + 5

The correct answer is B: x + 4 and x + 5. In a tile model, the x² tile comes from x multiplied by x. The two groups of x-tiles must have coefficients whose sum is 9, and the unit tiles must have a product of 20. The pair 4 and 5 satisfies both tests: 4 + 5 = 9 and 4 × 5 = 20. Thus x² + 9x + 20 factors as (x + 4)(x + 5). Option A has constants 1 and 20, whose product is 20, but their sum is 21, so its middle term would be 21x. Option C has sum 12, so it would produce x² + 12x + 20. Option D gives a sum of 29 and product 180, so neither coefficient matches. A useful method is to list factor pairs of the constant term first, then select the pair whose sum equals the coefficient of x. This is why the tile model supports factorisation rather than merely matching one number.