# Quadratic Equations - Nature of Roots

Ex 4.4 Q5. CBSE 10th Maths NCERT exercise solution

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

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 m2
Area = length × width = 400 m2
i.e., x × (40 – x) = 400
40x – x2 = 400
x2 – 40x + 400 = 0

In this equation, a = 1, b = -40, c = 400
Discriminant b2 - 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 m2.