Chapter 4: Quadratic Equations

Example – 13. Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth.

Solution :- 2(l + b ) = 80

Or, l + b = 40

Let l = x, then b = 40 – x

A/Q x(40 – x ) = 400

Or, 40x – x2 = 400

Or, x2 – 40x + 400 = 0

Here, a = 1, b = – 40, c = 400 ;

D = b2 – 4 ac = (– 40 )2 – 4 × 1 × 400

= 1600 – 1600

= 0 (positive).

Hence, it is possible.

By completing square, (x – 20 )2 = 0

Either, x – 20 = 0 or, x - 20 = 0

Or, x = 20, 20

Thus l = 20 m and b = 20 m.

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Subjects Maths (Part-1) by Mr. M. P. Keshari
Chapter 1 Linear Equations in Two Variables
Chapter 2 HCF and LCM
Chapter 3 Rational Expression
Chapter 4 Quadratic Equations
Chapter 5 Arithmetic Progressions
Chapter 6 Instalments
Chapter 7 Income Tax
Chapter 8 Similar Triangles