In a square with side (a+2b), what will be the total rectangular area involving (b)?
Answer and explanation
Correct answer: (4ab) / correct rectangular area
The side of the square is \(a+2b\), so the diagram can be viewed as two parts with lengths \(a\) and \(2b\) along each side. The rectangular regions involving these two different parts occur twice: one has dimensions \(a\) by \(2b\), and the other has the same dimensions. Each rectangle therefore has area \(a\cdot2b=2ab\).
Adding both rectangular areas gives \(2ab+2ab=4ab\). Equivalently, the cross term in \((a+2b)^2\) is \(2\cdot a\cdot2b=4ab\). The term \(4b^2\) is the square part formed by the \(2b\) sections, while \(a^2\) is the other square part. Hence option B, \(4ab\), is the total rectangular area involving \(b\).
Frequently asked questions
What is the correct answer to this question?
(4ab) / correct rectangular area
Why is this the correct answer?
The side of the square is \(a+2b\), so the diagram can be viewed as two parts with lengths \(a\) and \(2b\) along each side. The rectangular regions involving these two different parts occur twice: one has dimensions \(a\) by \(2b\), and the other has the same dimensions. Each rectangle therefore has area \(a\cdot2b=2ab\).
Adding both rectangular areas gives \(2ab+2ab=4ab\). Equivalently, the cross term in \((a+2b)^2\) is \(2\cdot a\cdot2b=4ab\). The term \(4b^2\) is the square part formed by the \(2b\) sections, while \(a^2\) is the other square part. Hence option B, \(4ab\), is the total rectangular area involving \(b\).
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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