Question

Is it possible to design a rectangular park of perimeter 80 m and area 400 sq m.​

Answer 1

Answer:

Given : a rectangular park of perimeter 80 m and area 400 m²

To find : is design possible ? find length & Breadth

Solution:

Let say Length = L

& Breadth = B

Perimeter = 80 m

=> 2(L + B) = 80

=> L + B = 40

=> L = 40 - B

Area = 400 m²

=> LB = 400

=> (40 - B)B = 400

=> 40B - B² = 400

=> B² - 40B + 400 = 0

=> ( B - 20)² = 0

=> B = 20

L = 40-B = 20

Length = 20 & Breadth = 20

YES , its possible to Design a rectangular Park of perimeter 80 m and area 400 m²

Note : (Square is a special Case of rectangle where adjacent sides are also equal )

Answer 2

Answer:

Step-by-step explanation:

Let x be the length and y be width of the rectangle

so the perimeter of rectangle will be, 2(x+y)=80, x+y=40..................(1)

Area of rectangle will be, xy=400, y=400/x now plug this in (1) we get,

x+400/x=40, x^2 -40x +400, we have a=1, b= -40, c=400

Now find the D=b^2 -4ac = (-40)^2 -4*1*400=1600-1600=0, Yes it is possible to a design a rectangle of the given specification but that will be a special rectangle called square of the dimensions : 20*20

so we have x=20, y=20