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

Solution:

Consider a rectangular park with length as 'l' and breadth as 'b' respectively.

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

Area of a rectangle = l × b = 400 ....(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 - b² = 400

40b - b² - 400 = 0

b² - 40b + 400 = 0

Let’s find the discriminant: b² - 4ac

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

b² - 4ac = (- 40)² - 4(1)(400)

= 1600 - 1600

= 0

Since, the value of the discriminant is 0, thus we can have two equal and real roots.

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

x = [- b ± √(b² - 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

Note that the park will be square in shape with side length 20 m.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 4

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Video Solution:

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

Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.4 Question 5

Summary:

Yes, it is possible to design a rectangular park of perimeter 80 m and area 400 m². The length and breadth both are equal to 40 m. Hence, the park will be square in shape.

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