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

**Solution:**

Perimeter of rectangle = 2(l + b) = 80 ....(1)

Area of rectangle = l × b = 400 ....(2)

We will use the 1st equation to express l in the form of b. Then, we will substitute this value of l in equation 2.

2(l + b) = 80

(l + b) = 40

l = 40 - b

Substituting the value of l = 40 - b in equation (2)

(40 - b)(b) = 400

40b - b^{2} = 400

40b - b^{2} - 400 = 0

b^{2} - 40b + 400 = 0

Let’s find the discriminant: b^{2} - 4ac

a = 1, b = -40, c = 400

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

= 1600 - 1600

= 0

Therefore, it is possible to design a rectangular park with the given condition:

x = (-b ± √(b^{2} - 4ac)) / 2a

= (- b ± 0) / 2a

= (-(- 40)) / 2(1)

= 40 / 2

= 20

So, breadth of the rectangle is b = 20 m and its length is l = 40 - b = 20 m

Yes, it is possible.

**Video Solution:**

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

### Class 10 Maths NCERT Solutions - Chapter 4 Exercise 4.4 Question 5:

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

Yes, it is possible to design a rectangular park with the given condition as a rectangular park with a perimeter of 80 m and an area of 400. The length and breadth both are equal to 40 m.