The length and the breadth of a rectangular garden are in the ratio 9 :5. A path 3.5 m wide, running all around inside it has an area of 1911 m2. Find the dimensions of the garden.

Given:


Length : Breadth 9 : 5


Width of the path = 3.5 m


Area of path = 1911 m2


Let,


Length of field = 9x


Breadth of field = 5x



Area of field = Length × Breadth


= 9x × 5x


= 45 x2


Therefore,


Length of field without path = 9x - (3.5 + 3.5)


= 9x - 7


Breadth of field without path = 5x - (3.5 + 3.5)


= 5x - 7


Therefore,


Area of field without path = Length without path × Breadth without path


= (9x - 7) × (5x - 7)


= 45x2 – 35x – 63x + 49


= 45x2 – 98x + 49


Now,


Area of path = Area of field - Area of field without path


1911 = 45 x2 – (45x2 – 98x + 49)


1911 = 45 x2 – 45x2 + 98x - 49


1911 = 98x - 49


98x = 1911 + 49


98x = 1960


x = 20


Hence,


Length of field = 9x = 9 × 20 = 180 m


Breadth of field = 5x = 5 × 20 = 100 m


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