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Quadratic Equations
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30/05/2021 12:17 pm
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Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.
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30/05/2021 12:18 pm
Let the length and breadth of the park be l and b.
Perimeter of the rectangular park = 2 (l + b) = 80
So, l + b = 40
Or, b = 40 – l
Area of the rectangular park = l × b = l(40 – l) = 40l – l2 = 400
l2 – 40l + 400 = 0, which is a quadratic equation.
Comparing the equation with ax2 + bx + c = 0, we get
a = 1, b = -40, c = 400
Since, Discriminant = b2 – 4ac
=(-40)2 – 4 × 400
= 1600 – 1600 = 0
Thus, b2 – 4ac = 0
Therefore, this equation has equal real roots. Hence, the situation is possible.
Root of the equation,
l = –b/2a
l = (40)/2(1) = 40/2 = 20
Therefore, length of rectangular park, l = 20 m
And breadth of the park, b = 40 – l = 40 – 20 = 20 m.