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QOTD #10 The length of each side of rectangle R is integer
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14 Aug 2016, 06:52
14 Aug 2016, 06:52
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Question Stats:
73% (01:17) correct
26% (01:23) wrong based on 289 sessions
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The length of each side of rectangle R is an integer, and the area of R is 36.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
Number of possible values of perimeter of R |
6 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Practice Questions
Question: 3
Page: 149
Question: 3
Page: 149
Re: QOTD #10 The length of each side of rectangle R is integer
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14 Aug 2016, 06:52
14 Aug 2016, 06:52
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Expert Reply
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Explanation
Because the length of each side of rectangle R is an integer and each length is a factor of the area 36, there are 5 possible rectangles: a 1 × 36 rectangle, a 2 × 18 rectangle, a 3 x 12 rectangle, a 4 × 9 rectangle, and a 6 × 6 rectangle.
The perimeter of the 1 × 36 rectangle is 2(1 + 36), or 74.
The perimeter of the 2 × 18 rectangle is 2(2 + 18), or 40.
The perimeter of the 3 × 12 rectangle is 2(3 + 12), or 30.
The perimeter of the 4 × 9 rectangle is 2(4 + 9), or 26.
The perimeter of the 6 × 6 rectangle is 2(6 + 6), or 24.
Since each of the 5 possible rectangles has a different perimeter, Quantity A, the number of possible values of the perimeter, is 5. Since Quantity B is 6, the correct answer is Choice B.
Because the length of each side of rectangle R is an integer and each length is a factor of the area 36, there are 5 possible rectangles: a 1 × 36 rectangle, a 2 × 18 rectangle, a 3 x 12 rectangle, a 4 × 9 rectangle, and a 6 × 6 rectangle.
The perimeter of the 1 × 36 rectangle is 2(1 + 36), or 74.
The perimeter of the 2 × 18 rectangle is 2(2 + 18), or 40.
The perimeter of the 3 × 12 rectangle is 2(3 + 12), or 30.
The perimeter of the 4 × 9 rectangle is 2(4 + 9), or 26.
The perimeter of the 6 × 6 rectangle is 2(6 + 6), or 24.
Since each of the 5 possible rectangles has a different perimeter, Quantity A, the number of possible values of the perimeter, is 5. Since Quantity B is 6, the correct answer is Choice B.
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Re: QOTD #10 The length of each side of rectangle R is integer
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25 Jan 2017, 09:11
25 Jan 2017, 09:11
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roshangre wrote:
Why the length can't more than 7? Say, if length=7, breadth will be 36/7 and so on ? The information is only about length being an integer, it hasn't said anything about breadth, I mean it doesnot say if breadth is an integer as well.
When we are growing up, we learn that the area of a rectangle is length x width, and this sets us up to have incorrect theories concerning what we call the sides of a rectangle.
Many people call the vertical side the length and the horizontal side the width. Others call the longest side the length and the shortest side the width.
None of this is true.
Length does not refer to the arbitrary side of a rectangle. Length refers to the distance from one point to another.
The question says, "The length of each side of rectangle R is an integer, and the area of R is 36"
The word length is not referring to a specific side of the rectangle; it is referring to every side of the rectangle.
I hope that helps.
Cheers,
Brent
