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The diagram below shows a rectangular garden, bordered by a walkway...

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The diagram below shows a rectangular garden, bordered by a walkway...

by BTGmoderatorLU » Tue Jan 21, 2020 5:49 am
Source: Manhattan Prep

The diagram below shows a rectangular garden, bordered by a walkway consisting of white and gray rectangles. If all four of the gray rectangles have the same dimensions, and the garden measures 20 by 10 feet, what is the area of the walkway?

1) Each gray rectangle has area 12 square feet.
2) The outer perimeter of the walkway is 88 feet.

The OA is E
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Re: The diagram below shows a rectangular garden, bordered by a walkway...

by Jay@ManhattanReview » Tue Jan 21, 2020 9:47 pm
BTGmoderatorLU wrote: ↑
Tue Jan 21, 2020 5:49 am
 Source: Manhattan Prep

The diagram below shows a rectangular garden, bordered by a walkway consisting of white and gray rectangles. If all four of the gray rectangles have the same dimensions, and the garden measures 20 by 10 feet, what is the area of the walkway?

1) Each gray rectangle has area 12 square feet.
2) The outer perimeter of the walkway is 88 feet.

The OA is E
Let's take each statement one by one.

1) Each gray rectangle has area 12 square feet.

Say the side of the gray rectangle, along the 20 feet side of the garden is x feet, thus, the side of the gray rectangle, along the 10 feet side of the garden would be 12/x feet.

Since we do not have information about x, we can't get the unique value of x. Insufficient

2) The outer perimeter of the walkway is 88 feet.

Certainly insufficient.

(1) and (2) together

From (1), we know that one of the sides of the outer of the walkway = x + 20 + x = 20 + 2x; thus, the other side of the outer of the walkway = 12/x + 10 + 12/x = 10 + 24/x

Thus, the outer perimeter of the walkway = 2[(20 + 2x) + (10 + 24/x)] = 88

Upon solving the above quadratic equation, we get x = 3 or 4

• Taking x = 3, we have two sides of the outer of the walkway: 26 and 18, thus, area = 26*18 = 468;

• Taking x = 4, we have two sides of the outer of the walkway: 28 and 16, thus, area = 26*18 = 448

No unique answer. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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