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.

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Solution

## Let the length and breadth of the garden be 9x m and 5x m, respectively, Now, Area of the garden = $\left(9x×5x\right)=45{x}^{2}$ Length of the garden excluding the path = ($9x-7\right)$ Breadth of the garden excluding the path = $\left(5x-7\right)$ Area of the path = $45{x}^{2}-\left[\left(9x-7\right)\left(5x-7\right)\right]$ $⇒1911=45{x}^{2}-\left[45{x}^{2}-63x-35x+49\right]\phantom{\rule{0ex}{0ex}}⇒1911=45{x}^{2}-45{x}^{2}+63x+35x-49\phantom{\rule{0ex}{0ex}}⇒1911=98x-49\phantom{\rule{0ex}{0ex}}⇒1960=98x\phantom{\rule{0ex}{0ex}}⇒x=\frac{1960}{98}\phantom{\rule{0ex}{0ex}}⇒x=20$ Thus, we have: Length = $9x=20×9=180\mathrm{m}$ Breadth = $5x=5×20=100\mathrm{m}$

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