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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. Q.5

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How i solve the question of quadratic equation of exercise 4.4 of class 10th math. The best way for solving this question is 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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1. 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) = 40– 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, = 20 m

And breadth of the park, = 40 – = 40 – 20 = 20 m.

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