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Question

The length an 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.

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Solution

Given: Length and breadth of the rectangular garden are in the ratio 9: 5 and the width of the path is 3.5 m.

Let the length and breadth of the garden be 9xand 5x respectively.

The length and breadth of the inner rectangle are

9x2×3.5 and 5x2×3.5

ie, 9x7 and 5x7

Now area of garden =9x×5x=45x2

and area of the inner rectangle =(9x7)(5x7)

=45x263x35x+49

=45x298x+49

also the area of path = 1911 m2

45x2(45x298x+49)=1911

98x49)=1911

49(2x1)=1911

2x1=39

2x=40x=20

Length =9x=9×20=180

Breadth =5x=5×20=100


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