Question

The perimeter of a rectangular plot is 62 m and its area is 288 sq meters. Find the dimension of the plot

Answer 1

Let the length and breadth of the rectangular plot be x and y meter, respectively. Therefore, we have 

Perimeter=`2(x+y)=62` 

Area =`xy=228` 

⇒` y=228/x` 

Putting the value of y in (i), we get 

⇒`2(x+228/x)=62` 

⇒` x+228/x=31` 

⇒`x^2+228=31x` 

⇒`x^2-31x+228=0` 

⇒`x^2-(19+12)x+228=0` 

⇒`x^2-19x-12x+228=0` 

⇒`x(x-19)-12(x-19)=0` 

⇒`(x-19)(x-12)=0` 

⇒`x=19  or  x=12` 

If` x=19 m , y=228/19=12 m` 

Therefore, the length and breadth of the plot are 19 m and 12 m, respectively.