In a rectangle with sides (x+1) and (x+9), what will be the sum of middle strips?
Answer and explanation
Correct answer: \(10x\)
Dividing the rectangle according to \(x+1\) and \(x+9\) produces four smaller areas: \(x^2\), \(9x\), \(x\), and \(9\). The two middle strips have areas \(9x\) and \(x\), so their sum is \(9x+x=10x\). \(9x\) represents only one middle strip, not their combined area. Exam tip: In a visual model, find each small rectangle’s area separately before combining like terms.
Frequently asked questions
What is the correct answer to this question?
\(10x\)
Why is this the correct answer?
Dividing the rectangle according to \(x+1\) and \(x+9\) produces four smaller areas: \(x^2\), \(9x\), \(x\), and \(9\). The two middle strips have areas \(9x\) and \(x\), so their sum is \(9x+x=10x\). \(9x\) represents only one middle strip, not their combined area. Exam tip: In a visual model, find each small rectangle’s area separately before combining like terms.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Visual models of identities.
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