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Question
The length and 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 `1911m^2` . Find the dimensions of the garden.
Solution
Let the length and breadth of the garden be 9x m and 5x m, respectively, Now,
Area of the garden=`(9x xx 5x)45x^2`
Length of the garden excluding the path =`(9x-7)`
Breadth of the garden excluding the path =`(5x-7)`
Area of the path = `45x^2=[(9x-7)(5x-7)]`
⇒ `1911=45x^2-[45x^2-63x-35x+49]`
⇒`1911=45x^2-45x^2+63x+35x-49`
⇒`1911=98x-49`
⇒`1960=98x`
⇒`x=1960/98`
⇒ `x=20`
Thus, we have:
Length=`9x=20xx9=180m`
Breadth=`5x=5xx20=100m`
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