Question

13. 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 m
Find the dimensions of the garden.
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Answer 1

Let the length and breadth of a rectangular garden be 9x and 5x.

Area of field = Length × Breadth=9×(5x) =45x2

Length of field without path =9x−(3.5+3.5)=9x−7

Breadth of field without path =5x−(3.5+3.5)=5x−7

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

=(9x−7)×(5x−7)

=45x 2

−35x−63x+49

=45x 2

−98x+49

Now,

Area of path = Area of field − Area of field without path

1911=45x 2

−(45x2

−98x+49)

1911=98x−49

x=20

Therefore:

Length of field =9x=9×20=180m

Breadth of field =5x=5×20=100m

Step-by-step explanation:

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