If the tile model of \(x^2+9x+20\) forms a complete rectangle, which arrangement is correct?

Correct answer: Sides \((x+4)\) and \((x+5)\)

The correct answer is A: the rectangle has sides \((x+4)\) and \((x+5)\). Multiply them carefully: \((x+4)(x+5)=x^2+5x+4x+20=x^2+9x+20\). In a tile model, the \(x^2\) tile is the large corner square, the \(5x\) and \(4x\) tiles form the two linear strips, and the unit tiles make the corner area 20. Thus the numbers must have both sum 9 and product 20; 4+5=9 and 4×5=20. B has product 20 but sum 12, so it gives \(x^2+12x+20\). C gives \(x^2+29x+180\), and D gives \(x^2+21x+20\), so neither matches. A complete rectangle requires matching every tile, not merely the constant term. Memory cue: for \(x^2+px+q\), choose numbers adding to p and multiplying to q.