Question

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.

Answer 1

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`