What is the area of a rectangle with length \(x+2\) and breadth \(x+5\) in visual form?

Correct answer: \(x^2+7x+10\)

The direct answer is D: \(x^2+7x+10\). The area of a rectangle is length multiplied by breadth, so calculate \((x+2)(x+5)\). A visual model divides the rectangle into four parts: an \(x\times x\) square with area \(x^2\), an \(x\times5\) rectangle with area \(5x\), a \(2\times x\) rectangle with area \(2x\), and a \(2\times5\) rectangle with area 10. Adding all parts gives \(x^2+5x+2x+10=x^2+7x+10\). A has the correct middle coefficient but the wrong constant term; 2 times 5 is 10, not 7. B incorrectly uses 10x as the middle term and also has the wrong constant. C uses only 3x for the two middle rectangles, although their total is 5x+2x=7x. D correctly includes every region of the model. Memory cue: for \((x+r)(x+s)\), the constant term is \(rs\) and the middle coefficient is \(r+s\).