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17 May 2024, 13:10
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Question Stats:
66% (03:00) correct
33% (00:57) wrong based on 3 sessions
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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?
=?square feet
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GMAT-Club-Forum-3dbg27xz.jpeg [ 11.4 KiB | Viewed 539 times ]
19 May 2024, 12:12
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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.
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.
At this point, we can see that the total length of region A = 18 + 3 + 3 = 24 feet
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.
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
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.
At this point, we can see that the total length of region A = 18 + 3 + 3 = 24 feet
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.
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
28 Jul 2024, 11:41
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Official Explanation
You can see from the figure that the shaded region is the region between the two rectangles. Looking at the shaded region in this way suggests that the area of the walkway can be calculated as the difference between the area of the larger rectangle and the area of the smaller rectangle.
The region represented by the smaller rectangle is the garden. Since the garden is 18 feet long and 12 feet wide, its area is (18)(12), or 216 square feet. 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 18 + (2)(3) = 24 feet. The width of the region is the width of the garden plus twice the width of the walkway, or 12 + (2)(3) = 18 feet. 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 432 - 216, or 216 square feet.
Another way to approach this problem is to think of the walkway as being composed of four rectangles and four squares, as shown in the figure below.
Each of the four squares is 3 feet long and 3 feet wide. The two rectangles running along the length of the garden are 18 feet long and 3 feet wide, and the two rectangles running along the width of the garden are 12 feet long and 3 feet wide. Thus, the area of the walkway is 4(3)(3) + 2(18)(3) + 2(12)(3) = 36 + 108 + 72 = 216 square feet
The correct answer is 216.
You can see from the figure that the shaded region is the region between the two rectangles. Looking at the shaded region in this way suggests that the area of the walkway can be calculated as the difference between the area of the larger rectangle and the area of the smaller rectangle.
The region represented by the smaller rectangle is the garden. Since the garden is 18 feet long and 12 feet wide, its area is (18)(12), or 216 square feet. 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 18 + (2)(3) = 24 feet. The width of the region is the width of the garden plus twice the width of the walkway, or 12 + (2)(3) = 18 feet. 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 432 - 216, or 216 square feet.
Another way to approach this problem is to think of the walkway as being composed of four rectangles and four squares, as shown in the figure below.
Each of the four squares is 3 feet long and 3 feet wide. The two rectangles running along the length of the garden are 18 feet long and 3 feet wide, and the two rectangles running along the width of the garden are 12 feet long and 3 feet wide. Thus, the area of the walkway is 4(3)(3) + 2(18)(3) + 2(12)(3) = 36 + 108 + 72 = 216 square feet
The correct answer is 216.
Attachment:
GMAT-Club-Forum-qltcfb9f.jpeg [ 12.35 KiB | Viewed 512 times ]
