**Nature of Roots of Quadratic Equation:**

**CBSE Ncert Solutions Chapter 4 Quadratic Equations Exercise 4.4 Question 5 **

**5. Is it possible to design a rectangular park of perimeter metres and area . If so, find its length and breadth.**

**Solution:**

Let length of park = metres

We are given area of rectangular park =

Therefore, breadth of park = metres {Area of rectangle = length }

Perimeter of rectangular park = metres

We are given perimeter of rectangle = metres

**Therefore, we can write**

**Comparing equation,** **with general quadratic equation** , we get

and .

**Discriminant is equal to 0. Therefore, two roots of equation are real and equal which means that it is possible to design a rectangular park of perimeter 80 metres and area .**

**Using quadratic formula** **to solve equation, we get**

Here, both the roots are equal to .

**Therefore, length of rectangular park = metres**

**Breadth of rectangular park = metres **