Question

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

Answer 1

Answer:

perimeter = 80 m

area = 400

lenght =?

breadth =?

1. suppose we guess 20 ✖ 20= 400
2. and 20 + 20 ✖ 2 = 80
3. then the answer is correct
4. length = 20
5. breadth = 20

Answer 2

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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 – L^2 = 400

L^2 – 40 L + 400 = 0,

which is a quadratic equation.

Comparing the equation with ax^2 + bx + c = 0, we get

a = 1, b = -40, c = 400

Since, Discriminant = b2 – 4ac

=>(-40)^2 – 4 × 400

=> 1600 – 1600

= 0

Thus, b^2 – 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

Hope It's Helpful....:)