Question

The length an 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 $m^2$.Find the dimensions of the garden.

Answer 1

Given: Length and breadth of the rectangular garden are in the ratio 9: 5 and the width of the path is 3.5 m.

Let the length and breadth of the garden be 9xand 5x respectively.

The length and breadth of the inner rectangle are

$9x–2\times 3.5$ and $5x–2\times 3.5$

ie, $9x–7$ and $5x–7$

Now area of garden $=9x\times 5x=45x^2$

and area of the inner rectangle $=(9x–7)(5x–7)$

$=45x^2–63x–35x+49$

$=45x^2–98x+49$

also the area of path = 1911 $m^2$

⇒ $45x^2–(45x^2–98x+49)=1911$

⇒ $98x-49)=1911$

⇒ $49(2x–1)=1911$

⇒ $2x–1=39$

⇒ $2x=40\Rightarrow x=20$

Length $=9x=9\times 20=180$

Breadth $=5x=5\times 20=100$