# 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. - Mathematics

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

Concept: Area of Circle
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 17 Perimeter and Areas of Plane Figures
Q 13