Question 5:
Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.
Answer
Let the length and breadth of the park be l and b.
Perimeter = 2 (l + b) = 80
l + b = 40
Or, b = 40 − l
Area = l × b = l (40 − l) = 40l − l2
40l − l2 = 400
l2 − 40l + 400 = 0
Comparing this equation with
al2 + bl + c = 0, we obtain
a = 1, b = −40, c = 400
Discriminate = b2 − 4ac = (− 40)2 −4 (1) (400) = = 1600 − 1600 = 0
As b2 − 4ac = 0,
Therefore, this equation has equal real roots. And hence, this situation is possible.
Root of this equation,
l =−(b/2a)
Therefore, length of park, l = 20 m
And breadth of park, b = 40 − l = 40 − 20 = 20 m
Latest Govt Job & Exam Updates: