Question

is it possible to design a rectangular Park of perimeter 80m and area 300m square

Answer 1

perimeter = 80m area = 300m^2
2 ( l + b ) = 80 l * b = 300
( l + b ) = 40 l = 300 / b ----1 eq.
put value of l from eq. 1
300 / b + b = 40
300 + b^2 = 40b
b^2 - 40b +300 = 0
b^2 - 30b - 10b +300 = 0
b (b -30) -10 (b - 30) = 0
b - 10 = 0 b - 30 = 0
b = 10m b = 30m

From here,
length of rectangle = 300 / 10 = 30m and
300 / 30 = 10 m

yes it is possible...to draw a rectangle of length 30 m and breadth 10m.
Orr length of rectangle 10m and breadth 30m.

Answer 2

Answer:

yes

Step-by-step explanation:

Let the length be l m and the breadth be b m.

Then the area would be lb=400

Perimeter would be 2(l+b)=80

lb=400

⇒2(l+b)=80

⇒l+b=40

∴b=40−l --(1)

Substituting (1) in Area, we get

⇒l(40−l)=400

⇒40l−l

2

=400

⇒l

2

−40l+400=0

⇒(l−20)(l−20)=0

∴l=20

has equal roots, so it is possible to design the rectangle of given parameters.

⇒b=40−20=20

We now know that the length of the park is 20 m and the breadth of the park is also 20 m.