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Question 9 - End-of-Chapter Exercises - Chapter 4 Class 9 - Exploring Algebraic Identities (Ganita Manjari I)
Last updated at May 18, 2026 by Teachoo
End-of-Chapter Exercises
Class 9
Chapter 4 Class 9 - Exploring Algebraic Identities (Ganita Manjari I)
- Consecutive Square Numbers
- Visualising Algebraic Identities
- Exercise Set 4.1
- Factorisation of Algebraic Expressions Using Identities
- Exercise Set 4.2
- More Identities
- Exercise Set 4.3
- Rewriting a2 - b2 Identity
- Factorisation Using Algebra Tiles
- Factorisation by Splitting the Middle term
- Exercise Set 4.4
- Finding New Algebraic Identities
- Simplifying Rational Expressions
- Exercise Set 4.5
- Word Problems
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End-of-Chapter Exercises
Transcript
Question 9 A rectangular pool has area 2𝑥^2+7𝑥+3 square hastas. If its width is 2𝑥+1 hastas, find its length. Hasta was a unit used to measure length. We know that Area of rectangle = Length × Breadth 𝟐𝒙^𝟐+𝟕𝒙+𝟑 = Length × (𝟐𝒙+𝟏) Thus, we need to factorise 𝟐𝒙^𝟐+𝟕𝒙+𝟑 Now, 𝟐𝒙^𝟐+𝟕𝒙+𝟑 Factorising by Splitting the middle term = 2𝑥^2+𝟔𝒙+𝒙+3 = 2𝑥(𝑥+3)+1(𝑥+3) = (𝟐𝒙+𝟏)(𝒙+𝟑) Since Width = (𝟐𝒙+𝟏) Thus, Length = (𝐱+𝟑) hastas Splitting the middle term method We need to find two numbers whose Sum = 7 Product = 2 × 3 = 6 Since sum is negative but product is positive. Thus, both numbers are positive
