Why do two rectangles of area \(ab\) appear in the visual model of a square with side \(a+b\)?
Answer and explanation
Correct answer: Because the sides \(a\) and \(b\) combine in two directions to form two \(ab\) regions.
When the square is split using lengths \(a\) and \(b\), two mixed regions are formed: \(a\times b\) and \(b\times a\). Each has area \(ab\), giving \(2ab\). Exam tip: always count both rectangles.
Frequently asked questions
What is the correct answer to this question?
Because the sides \(a\) and \(b\) combine in two directions to form two \(ab\) regions.
Why is this the correct answer?
When the square is split using lengths \(a\) and \(b\), two mixed regions are formed: \(a\times b\) and \(b\times a\). Each has area \(ab\), giving \(2ab\). Exam tip: always count both rectangles.
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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