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.