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Ex 4.4, 5 - Is it possible to design a rectangular park - Mix questions - Equation to be formed

Ex 4.4, 5 - Chapter 4 Class 10 Quadratic Equations - Part 2

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Ex 4.4 ,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 = 0 – 40x + x2 + 400 = 0 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 So, the roots of the equation are So, x = 20 is the solution ∴ Length = x = 20 m Breadth = 40 – x = 40 – 20 = 20 m

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.