CBSE Class 10 Answered

Let length of rectangular plot = l cm

And breadth of rectangular plot =  b cm

Perimeter of rectangulat plot = 180 m

Therefore  2(l + b) = 180 m

                      l + b = 90

                      l = 90 - b                                  ......(i)

 Given area of rectangular plot = 1800

Therefore  l  b = 1800

      (90 - b )b = 1800                                                                     [from (i)]

90b - b^{2 =} 1800

b² - 90b +1800 = 0

b² - 60b - 30b  +1800 = 0

b(b - 60 ) - 30(b - 60 ) = 0

(b - 30)(b - 60 ) = 0

b - 30 = 0   and b - 60 = 0

b = 30 and b = 60

 When b = 30 m

  l = 90 - 30 m                             [ By putting value of b in (i)]

     = 60  m

When b = 60 m

l = 90 - 60 = 30 m                     [By putting value in (i)]

Neglecting  b = 60 m and l  =30m               [   length of rectangle cannot be less than breadth.]    

 Length  of rectangular plot = 60 m

And breadth of rectanular plot = 30 m.