Question

Is it possible to design a rectangular park of perimeter 320 m and area 4800 m²? If so find its length and breadth.

Answer 1

Let the length of the rectangular park be “l”

and the breadth of the rectangular park be “b”

Perimeter of the park = 320 m

2 (l + b) = 320

l + b = 160

l = 160 – b  ...(1)

Area of the park = 4800 m²

l × b = 4800  ...(2)

substitute the value of l = 160 – b in (2)

(160 – b)b = 4800

160b – b² = 4800

b² – 160b + 4800 = 0

(b – 120) (b – 40) = 0

b = – 120 = 0 or b – 40 = 0

b = 120 or b = 40

If breadth is 120 length is 40

If breadth is 40 length is 120

Length of the park = 120 m

Breadth of the park = 40 m