Question 9 - End-of-Chapter Exercises - Chapter 4 Class 9 - Exploring Algebraic Identities (Ganita Manjari I)

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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