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 metre square. find the dimensions of the garden​

Answer 1

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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 metre square. find the dimensions of the garden

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Let the length and breadth of a rectangular garden be 9x and 5x.

Area of field = Length × Breadth=9×(5x) =45x²

Length of field without path =9x−(3.5+3.5)=9x−7

Breadth of field without path =5x−(3.5+3.5)=5x−7

Area of field without path = Length without path x Breadth without path,

=(9x−7)×(5x−7)

= 45x² −35x−63x+49

=45x² −98x+49

Now,

Area of path = Area of field − Area of field without path,

1911 = 45x²− (45x²−98x+49)

➡️ 1911 = 98x−49

➡️ x = 20

Therefore:

Length of field =9x=9×20=180m

Breadth of field =5x=5×20=100m

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Answer 2

Step-by-step explanation:

Let, the length and breadth of garden be 9x and 5x ,

Path ( d) = 3.5m

Then,

area of garden = 1911 m²

So ,

According to formula,

Path of area out side = 2d( l + b + 2d)

1911m² = 2× 3.5m ( 9x + 5x + 2×3.5m)

1911m² = 7m ( 14x + 7m)

1911m² = 98mx + 49m²

1911m² - 49m² = 98mx

1813m² = 98mx

x = 1813m²/98m

x= 18.5 m

Hence,

length = 9x = 9 × 18.5 = 166.5m

breadth = 5x = 5× 18.5 = 92.5 m