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