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Class 9MathematicsExploring Algebraic IdentitiesVisual models of identitiesEasy
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In a square with side (3x+2), what will be the area of the small square?

Answer and explanation

Correct answer: 4

The direct answer is B: 4. In the visual model for (3x+2)², the large square is divided using lengths 3x and 2. The small corner square has side 2, so its area is 2×2=4. A, 2, is only the side length, not the area. B is correct because the area of a square is the square of its side. C, 6x, is the area of each mixed rectangle with sides 3x and 2, since (3x)(2)=6x; it is not the small corner square. D, 9x², is the area of the large 3x by 3x square. The complete identity is (3x+2)² = 9x²+12x+4, where the two mixed rectangles together contribute 12x. Thus the constant corner part must be 4. Memory cue: in a two-part square model, square each piece for the corner squares and multiply unlike pieces for the rectangles.

Related tags

Area-ModelSmall-SquareBinomial-SquareVisual-IdentityVisual Models Of IdentitiesExploring Algebraic IdentitiesMathematicsClass 9 Mcq
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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 × b is removed. The remaining area is related to which expression?
  5. 5In a visual model, a²−b² 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 large \(a\times a\) 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 eight \(x\)-tiles. If there are 16 constant tiles, what complete square does the model represent?
  10. 10If, in a square model, the total area of the two middle rectangles is \(10x\) and the small square has area 25, what is the side of the complete square?
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