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 = $(9x\times 5x)=45x^2$
Length of the garden excluding the path = ($9x-7)$
Breadth of the garden excluding the path = $(5x-7)$
Area of the path = $45x^2-\left[(9x-7)(5x-7)\right]$
$$\begin{gathered} \Rightarrow 1911=45x^2-\left[45x^2-63x-35x+49\right] \\ \Rightarrow 1911=45x^2-45x^2+63x+35x-49 \\ \Rightarrow 1911=98x-49 \\ \Rightarrow 1960=98x \\ \Rightarrow x=\frac{1960}{98} \\ \Rightarrow x=20 \end{gathered}$$
Thus, we have:
Length = $9x=20\times 9=180\mathrm{m}$
Breadth = $5x=5\times 20=100\mathrm{m}$