Question

Is it possible to design a rectangular Park of perimeter 80km and of area 400 square metres?
If possible, find out its length and breadth.

Answer 1

Perimeter of rectangular park = 80 metres

2(l+b) = 80

l+b = 80/2 =  40 M

l = (40-b)

$\rule{200}{2}$

we know that :-

Area of rectangle = length*Breadth

$Area = lb \\ \\ \\Area = (40-b)b\\ \\ \\40b-b^{2} = 400\\ \\ \\b^{2}-40b+400 = 0\\ \\ \\D=b^{2}-4ac= (-40)^{2}-4(400)\\ \\ \\D=1600-1600=0\\ \\ \\Hence,Real\:roots\:exists\:for\:it$

$\rule{200}{2}$

$b^{2}-40b+400 = (b-20)^{2}\\ \\ \\ \implies b=20 metres$

$\rule{200}{2}$

Thus ,

The dimensions of the rectangle are :-

length = 20M

breadth = 20 M

$\rule{200}{2}$

This special type of rectangle is called as a SQUARE.

Hence , It is possible to design the park of the given dimensional areas and perimeter.

$\rule{200}{2}$

Answer 2

Step-by-step explanation:

Perimeter of rectangular park = 80 metres

2(l+b) = 80

l+b = 80/2 = 40 M

l = (40-b)

we know that :-

Area of rectangle = length*Breadth