Question 5 - End-of-Chapter Exercises - Chapter 4 Class 9 - Exploring Algebraic Identities (Ganita Manjari I)

Transcript

Question 5 (i) Find possible expressions for the length and breadth of each of the following rectangles whose areas are given by the following expressions in square units. (i) 25𝑎^2−30𝑎𝑏+9𝑏^2 Because Area = Length × Breadth We factor the expression into 2 brackets to give us Length and Breadth Now, our expression is 25𝑎^2−30𝑎𝑏+9𝑏^2 =25𝑎^2+9𝑏^2−30𝑎𝑏 =(𝟓𝒂)^𝟐+(𝟑𝒃)^𝟐−𝟐 × 𝟓𝒂 × 𝟑𝒃 Using (𝑎−𝑏)^2 = 𝑎^2 + 𝑏^2 – 2ab Where 𝑎 = 5𝑎, b = 3𝑏 =(5𝑎−3𝑏)^2 =(𝟓𝒂−𝟑𝒃)(𝟓𝒂−𝟑𝒃) Thus, Length = (𝟓𝒂−𝟑𝒃) Breadth = (𝟓𝒂−𝟑𝒃) Question 5 (ii) Find possible expressions for the length and breadth of each of the following rectangles whose areas are given by the following expressions in square units. (ii) 36𝑠^2−49𝑡^2 Because Area = Length × Breadth We factor the expression into 2 brackets to give us Length and Breadth Now, our expression is 36𝑠^2−49𝑡^2 =(𝟔𝒔)^𝟐−(𝟕𝒕)^𝟐 Using 𝑎^2−𝑏^2=(𝑎+𝑏)(𝑎−𝑏) Where 𝑎 = 6𝑠, b = 7𝑡 =(𝟔𝒔+𝟕𝒕)(𝟔𝒔−𝟕𝒕) Now, we can consider any bracket as length Thus, Length = (𝟔𝒔+𝟕𝒕) Breadth = (𝟔𝒔−𝟕𝒕)