Question

lt is possible to design a rectangular park of perimeter 80m and area 400m? lf so find its length and breadth.​

Answer 1

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Answer 2

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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 - l240l -  l2 = 400

l2 -  40l + 400 = 0

Comparing this equation with al2 + bl + c = 0, we get

a = 1, b = -40, c = 400

Discriminant = b2 - 4ac

(-40)2 - 4 × 400

= 1600 - 1600 = 0

b2 - 4ac = 0

Therefore, this equation has equal real roots. And hence, this situation is

possible Root of this equation,l = -b/2a

l = (40)/2(1) = 40/2 = 20

Therefore, length of park, l = 20 m

And breadth of park, b = 40 - l = 40 - 20 = 20 m.