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Ex 4.3, 5 Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth. Let Length be x Given that Perimeter = 80 m 2(Length + Breadth) = 80 m (Length + Breadth) = 80/2 (x + Breadth) = 40 Breadth = 40 – x Also, given that Area = 400 m2 Length × Breadth = 400 x (40 – x) = 400 40x – x2 = 400 40x – x2 – 400 = 0 0 = – 40x + x2 + 400 x2 – 40x + 400 = 0 We factorize by splitting the middle term x2 – 20x – 20x + 400 = 0 x (x – 20) – 20(x – 20) = 0 (x – 20) (x – 20) = 0 x – 20 = 0 x = 20 x – 20 = 0 x = 20 Splitting the middle term method We need to find two numbers whose Sum = – 40 Product = 400 × 1 = 400 So, the roots of the equation are 20, and 20 ∴ x = 20 is the solution Therefore, Length = x = 20 m Breadth = 40 – x = 40 – 20 = 20 m

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo