If rectangles of area (pq) are placed at opposite positions in a square of side (p+q), how many such rectangles will be present?
Answer and explanation
Correct answer: 2
When each side is divided into lengths \(p\) and \(q\), the square of side \(p+q\) is split into four regions: one square of area \(p^2\), one square of area \(q^2\), and two rectangles of area \(pq\) each. These two \(pq\) rectangles occupy diagonally opposite positions, so the answer is 2. Option 4 counts all regions of the figure, not just the \(pq\) rectangles. Exam tip: In \((p+q)^2=p^2+2pq+q^2\), \(2pq\) represents the combined area of the two rectangles.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
When each side is divided into lengths \(p\) and \(q\), the square of side \(p+q\) is split into four regions: one square of area \(p^2\), one square of area \(q^2\), and two rectangles of area \(pq\) each. These two \(pq\) rectangles occupy diagonally opposite positions, so the answer is 2. Option 4 counts all regions of the figure, not just the \(pq\) rectangles. Exam tip: In \((p+q)^2=p^2+2pq+q^2\), \(2pq\) represents the combined area of the two 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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