Question

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

Answer 1

Given: Perimeter of a rectangle 2(1 + b) = 80 

⇒ 6 + b = 80/2 = 40 

Area of the rectangle, l × b = 400 

If possible, let us suppose that length of the rectangle = x m say 

Then its breadth by equation (1) = 40 – x 

By problem area = x . (40 – x) = 400

⇒ 40x – x² = 400 

⇒ x² – 40x + 400 = 0 

Here a = 1; b = -40; c = +400 

b² – 4ac = (-40)² – 4(1)(+400) 

= 1600 – 1600 = 0 

∴ The roots are real and equal. 

They are \(\frac{-b}{2a}\), \(\frac{-b}{2a}\) 

i.e., \(\frac{-(-40)}{2\times1}\) = \(\frac{40}{2a}\) = 20 

∴ The dimensions are 20 m, 20 m. 

(∴ The park is in square shape)