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The figure above represents a rectangular garden with a walkw

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The figure above represents a rectangular garden with a walkw [#permalink] New post 14 Dec 2015, 06:51
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The figure above represents a rectangular garden with a walkway around it. The garden is 18 feet long and 12 feet wide. The walkway is uniformly 3 feet wide, and its edges meet at right angles. What is the area of the walkway?

\(\boxed {square feeet}\)

[Reveal] Spoiler:
216


Practice Questions
Question: 11
Page: 153
Difficulty: medium

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Re: The figure above represents a rectangular garden with a walkw [#permalink] New post 14 Dec 2015, 07:01
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Solution

The region represented by the larger rectangle is the garden and the walkway combined. The length of the region is the length of the garden plus twice the width of the walkway, or feet. The width of the region is the 18+(2)(3)=24 width of the garden plus twice the width of the walkway, or feet. 12+(2)(3)=18
Therefore, the area of the region represented by the larger rectangle is (24)(18), or 432 square feet, and the area of the walkway is or \(216\) square feet.
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Re: The figure above represents a rectangular garden with a walkw [#permalink] New post 23 May 2018, 09:15
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Carcass wrote:
Image

The figure above represents a rectangular garden with a walkway around it. The garden is 18 feet long and 12 feet wide. The walkway is uniformly 3 feet wide, and its edges meet at right angles. What is the area of the walkway?

Image

[Reveal] Spoiler:
216


Practice Questions
Question: 11
Page: 153
Difficulty: medium


Let's first add some lines to divide the walkway into 4 rectangular regions (A, B, C and D), and then find the area of each region.
Image

We'll start with region A.
Since the walkway is uniformly 3 feet wide, we can add this to our diagram.
We'll also add the fact that the garden is 18 feet long.
Image


At this point, we can see that the total length of region A = 18 + 3 + 3 = 24 feet
Image
So, the area of region A = (3)(24) = 72
Since region B is identical to region A, we know that the area of region B = 72 also


Now let's examine region C.
Image
We can see that the dimensions of region C are 3 by 12
So, the area of region C = (3)(12) = 36
Since region D is identical to region C, we know that the area of region D = 36 also

TOTAL AREA of walkway = 72 + 72 + 36 + 36 = 216

Answer: 216

Cheers,
Brent
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Re: The figure above represents a rectangular garden with a walkw [#permalink] New post 01 Aug 2019, 07:11
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(18+6)x(12+6)-18x12 = 216 ans.
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Re: The figure above represents a rectangular garden with a walkw [#permalink] New post 02 May 2020, 09:52
Hi,

Just one question, why we are adding length and width of garden when we have to find the area of only walkway?
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Re: The figure above represents a rectangular garden with a walkw [#permalink] New post 02 May 2020, 10:05
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Farina wrote:
Hi,

Just one question, why we are adding length and width of garden when we have to find the area of only walkway?


In order to find the area of a rectangle, we need the length and the width.
In a few places in my solution, we don't necessarily know the length and width.
Define those values, we sometimes have to add a few lengths together.

For example, in my solution, I write: At this point, we can see that the total length of region A = 18 + 3 + 3 = 24 feet

Does that help?
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Re: The figure above represents a rectangular garden with a walkw [#permalink] New post 15 May 2020, 05:45
Carcass wrote:
Solution

The region represented by the larger rectangle is the garden and the walkway combined. The length of the region is the length of the garden plus twice the width of the walkway, or feet. The width of the region is the 18+(2)(3)=24 width of the garden plus twice the width of the walkway, or feet. 12+(2)(3)=18
Therefore, the area of the region represented by the larger rectangle is (24)(18), or 432 square feet, and the area of the walkway is or \(216\) square feet.
Re: The figure above represents a rectangular garden with a walkw   [#permalink] 15 May 2020, 05:45
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