Question

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

Answer 1

Given:

➜ perimeter of Rectangle, P = 80 m

➜ area of rectangle, A = 400 m²

To Find:

➜ Length and breadth of the rectangle if possible

Solution:

Let the length and breadth of the rectangle be x and y respectively.

We know,

Perimeter = 2 { Length + Breadth }

☛ 80 = 2 { x + y }

☛ x + y = 40

☛ x = 40 - y ...(1)

Also,

Area = Length × Breadth

☛ 400 = x × y

☛ ( 40 - y ) y = 400

{ from (1), x = 40 - y }

☛ 40y - y² = 400

☛ y² - 40y + 400 = 0

☛ y² - 20y - 20y + 400 = 0

☛ y( y - 20) - 20( y - 20) = 0

☛ (y - 20)(y - 20) = 0

y = 20 and y = 20

Here, y = 20

Substituting value of y in (1), we get

☛ x = 40 - y

☛ x = 40 - 20

☛ x = 20

Since, the sides are equal, So it is a square shaped park and not a rectangular one.

Hence, It is not possible.

Answer 2

It is not a rectangular park it is square.