In a rectangle with sides \((x+1)\) and \((x+9)\), what is the sum of the two middle strips in the area model?

Correct answer: \(10x\)

Correct answer: B, \(10x\). In an area model, multiply the length of one side by the length of the corresponding part of the other side. Split the sides into \(x+1\) and \(x+9\). The four regions have areas \(x\cdot x=x^2\), \(x\cdot9=9x\), \(1\cdot x=x\), and \(1\cdot9=9\). The two middle strips are therefore \(9x\) and \(x\). Adding them gives \(9x+x=10x\). Option A, \(9x\), counts only one strip. Option B combines both middle strips and is correct. Option C is the large square-like term from multiplying \(x\) by \(x\), not a middle strip. Option D is the small corner area. Memory cue: the two cross-strips usually combine into the coefficient of the middle term.