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Class 9MathematicsExploring Algebraic IdentitiesVisual models of identitiesMedium
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If the area of a square model is 9x² + 24x + 16, what is its side length?

Answer and explanation

Correct answer: 3x + 4

The correct answer is A, 3x + 4. Since 9x² + 24x + 16 = (3x)² + 2(3x)(4) + 4² = (3x + 4)², the expression is the square of 3x + 4. Thus the side length is 3x + 4, assuming this expression is non-negative as a length must be.

Related tags

Perfect-Square IdentityArea ModelAlgebraic IdentitiesVisual ModelsVisual 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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