#### Question: Is it possible to design a rectangular park of perimeter 80 m and area 400 m^{2}? If so, find its length and breadth.

#### Explanatory Answer

Let the length of the park be x metres.

Given Information: Perimeter of the rectangular park is 80 m

Perimeter = 2 (length + width) = 80 m

∴ length + width = 40 m

Length = x. So, x + width = 40

Or width = (40 – x) m

Given Information: Area of the rectangular park is 400 m^{2}

Area = length × width = 400 m^{2}

i.e., x × (40 – x) = 400

40x – x^{2} = 400

x^{2} – 40x + 400 = 0

In this equation, a = 1, b = -40, c = 400

Discriminant b^{2} - 4ac = (-40)^{2} – 4 × 1 × 400

= 1600 - 1600 = 0

Discriminant is zero. So, the two roots are real and equal.

Length, x = \\frac{-(-40)}{2}) = \\frac{40}{2}) = 20 m

∴ width = 40 – x = 20 m

The rectangle is a square of side 20 m.

YES. It is possible to have a rectangular park of perimeter 80 m and area 400 m^{2}.