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

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 - l² = 400
→ l² - 40l + 400 = 0
→ (l - 20)(l - 20) = 0
∴ l = 20
It 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 20m and the breadth of the park is also 20m.