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The length and the breadth of a rectangular garden are in the

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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 $1911 m^{2}$ . Find the dimensions of the garden.

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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 m^{2}

. Find the dimensions of the garden.

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

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

Area of field

=

Length

\times

Breadth

= 9 \times (5 x)

= 45 x^{2}

Length of field without path

= 9 x - (3.5 + 3.5) = 9 x - 7

Breadth of field without path

= 5 x - (3.5 + 3.5) = 5 x - 7

Area of field without path

=

Length without path x Breadth without path

= (9 x - 7) \times (5 x - 7)

= 45 x^{2} - 35 x - 63 x + 49

= 45 x^{2} - 98 x + 49

Now,

Area of path

=

Area of field

-

Area of field without path

1911 = 45 x^{2} - (45 x^{2} - 98 x + 49)

1911 = 98 x - 49

x = 20

Therefore:

Length of field

= 9 x = 9 \times 20 = 180 m

Breadth of field

= 5 x = 5 \times 20 = 100 m

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Question Text	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 $1911 m^{2}$ . Find the dimensions of the garden.
Answer Type	Text solution:1
Upvotes	150

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 1911m2. Find the dimensions of the garden.

Text solutionVerified

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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 $1911 m^{2}$ . Find the dimensions of the garden.