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Class 9MathematicsExploring Algebraic IdentitiesVisual models of identitiesEasyLevel 69
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If the sides of a rectangle are (a+b) and (c), what two parts appear in the area model?

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Answer and explanation

Correct answer: Areas \(ac\) and \(bc\)

Splitting the side \(a+b\) into \(a\) and \(b\) divides the rectangle into two smaller rectangles. Each has the other side \(c\), so their areas are \(ac\) and \(bc\), respectively. Hence, the total area is \(c(a+b)=ac+bc\). \(a+b\) and \(c\) are the original side lengths, not the two area parts. Exam tip: in an area model, multiply the side lengths of each small rectangle.

Related tags

Algebraic IdentitiesDistributive PropertyArea ModelRectangle AreaVisual Algebra

Frequently asked questions

What is the correct answer to this question?

Areas \(ac\) and \(bc\)

Why is this the correct answer?

Splitting the side \(a+b\) into \(a\) and \(b\) divides the rectangle into two smaller rectangles. Each has the other side \(c\), so their areas are \(ac\) and \(bc\), respectively. Hence, the total area is \(c(a+b)=ac+bc\). \(a+b\) and \(c\) are the original side lengths, not the two area parts. Exam tip: in an area model, multiply the side lengths of each small rectangle.

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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