Question

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

Answer 1

Answer:

Hola‼.........❤✌

Let length of the rectangular park be x m and breadth be y m.

According to question,

perimeter = 80 m ⇒ 2(l + b) = 80 m

⇒ 2 (x + y) = 80

⇒ x + y = 40

=> y = 40-x

i.e, breadth =(40- x) m

Now, area = 400

=> l×b = 40

=> x (40-x) = 400

=> x^2 -40x +400 = 0

Here, a = 1, b = –40, c = 400

Now, D = b^2 – 4ac

 = (-40)^2 – 4(1) (400) = 1600 – 1600 = 0

Since, D=0

So, the given quadratic equation has equal roots and hence it is possible to design a rectangular park.

Now, solving the the quadratic equation x^2 - 40x +400 by quadratic formula, we get

x= -b +- √D/ 2a

= 40/2

= 20

Hence, length of the rectangular park, x = 20 m

& breath = (40-x) = 20 m

Hope it's helpful.... ☺