Question

Is it possible to design a rectangular park of perimeter 80 m and area 400 m². If so, find its length and breadth.

Answer 1

Solution :

Given : Perimeter of a rectangular Park = 80 m

Area of a rectangular Park = 400 m²

Let the breadth of the rectangular Park = x m

Perimeter of a rectangular Park = 80 m

2(Length + breadth) = 80 m

Length + breadth = 80/2= 40 m

Length + breadth = 40 m

Length + x = 40  

Length of the rectangular Park = (40 - x) m

Area of rectangular Park=  length × breadth

A.T.Q

400 = (40 - x ) × x

x² - 40x + 400 = 0

x² - 20x - 20x +400 = 0

[ By factorization]

x (x -20) -20(x -20)= 0

(x - 20) (x - 20) = 0

(x - 20)= 0 or  (x - 20) = 0

x = 20 or x= 20

Breadth of a rectangular Park = x = 20 m

Length of a rectangular Park =(40 - x) = 40 -20 = 20 m.

Hence, it is possible to design the rectangular Park having perimeter 80 m and Area 400 m² of equal length and breadth i e 20 m each  

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Answer:

Step-by-step explanation:

P of a rec = 2(l+b)

80=2(l+b)

40= l+ b .... eq 1

Now

Area of a rec= lb

400=lb

400/l=b... eq 2

Put the value of b in eq 2 from eq 1

40=l+b

40=l+400/l

L^2+400-40L= 0

L^2-40l+400=0

L^2-20l-20l+400=0

L(l-20)-20(l-20)=0

(l-20)( l-20)=0

So

L=20.

Now put the value of l in eq 2 thats is

400/20=b

20= b

Hope it helps u✌