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