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Class 9MathematicsExploring Algebraic IdentitiesVisual models of identitiesHardLevel 66
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A square of side (q) is removed from a square of side (p), and the remaining part is rearranged into a rectangle. What are the sides of the new rectangle?

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Answer and explanation

Correct answer: (p-q) and (p+q)

The removed-square model gives (p^2-q^2=(p-q)(p+q)). Exam tip: connect difference of squares with rectangle area.

Related tags

Difference Of SquaresRearrangementVisual Proof

Frequently asked questions

What is the correct answer to this question?

(p-q) and (p+q)

Why is this the correct answer?

The removed-square model gives (p^2-q^2=(p-q)(p+q)). Exam tip: connect difference of squares with rectangle area.

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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10 more MCQs
  1. 1A square has side \(a+b\). Which identity is shown by its area model?
  2. 2A diagram has two small squares with sides \(a\) and \(b\) and two equal rectangles. What is the total area?
  3. 3If the side of a big square is \(x+3\), how will its area be written?
  4. 4A square has side \(a\). A corner square of \(b \times b\) is removed. The remaining area is related to which expression?
  5. 5In a visual model \(a^2-b^2\) is rearranged into two rectangles. Which factorisation does it show?
  6. 6What is the area of a square with side \(a-b\)?
  7. 7In a diagram two \(a \times b\) rectangles are subtracted from a big \(a \times a\) square and a \(b \times b\) square is added back. Which identity is formed?
  8. 8What is the area of a rectangle with length \(x+2\) and breadth \(x+5\) in visual form?
  9. 9In a tile model there is one \(x^2\) tile and \(8\) \(x\)-tiles. If there are \(16\) constant tiles then the complete square models what?
  10. 10If in a square model the total area of the two middle rectangles is \(10x\) and the small square area is \(25\), what is the side?
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