Example 18 - Chapter 4 Class 9 - Exploring Algebraic Identities (Ganita Manjari I)

Transcript

Example 18 A rectangular pool is such that its breadth is 4 metres less than its length and its area is 96 sq. metres. Find the length and breadth of the pool. Let Length = x m Since its breadth is 4 metres less than its length Breadth = (x – 4) m So, our pool will look like Given that Area of rectangle = 96 m2 Length × Breadth = 96 𝒙 × (𝒙−𝟒)=𝟗𝟔 𝑥^2−4𝑥=96 𝒙^𝟐−𝟒𝒙−𝟗𝟔=𝟎 Factorising by splitting the middle term Since product is 96, and we need to find two numbers with product 96 We find prime factorisation of 96 𝑥^2−𝟏𝟐𝒙+𝟖𝒙−96=0 𝑥(𝑥−12)+8(𝑥−12)=0 (𝒙+𝟖)(𝒙−𝟏𝟐)=𝟎 Splitting the middle term method We need to find two numbers whose Sum = –4 Product = 1 × –96 = –96 Since both sum and product are negative. Thus, one number is positive, one is negative. And bigger is negative Thus, x + 8 = 0 x = –8 And, x – 12 = 0 x = 12 Since x = Length, it cannot be negative Thus, x = 12 Therefore, Length of rectangle = x = 12 m Breadth of rectangle = x – 4 = 12 – 4 = 8 m