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A triangle has sides 4, 7, and x. Which of the following could be the
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01 Jun 2023, 06:06
01 Jun 2023, 06:06
Expert Reply
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Question Stats:
66% (00:41) correct
33% (01:06) wrong based on 12 sessions
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A triangle has sides 4, 7, and x. Which of the following could be the perimeter of the triangle?
Indicate all such perimeters.
A. 13
B. 16
C. 17
D. 20
E. 22
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Indicate all such perimeters.
A. 13
B. 16
C. 17
D. 20
E. 22
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) Cracking the GRE Premium
\(\Longrightarrow\) GRE Math Essentials - A most comprehensive handout!!
Re: A triangle has sides 4, 7, and x. Which of the following could be the
[#permalink]
03 Jun 2023, 04:00
03 Jun 2023, 04:00
Expert Reply
OE
Remember the third side rule of triangles here, which is how to find possible lengths of the third side of a triangle when given the two other sides. The third side rule dictates that the length of the third side of a triangle must be greater than the difference, but less than the sum, of the length of the two known sides. In this particular problem, the two known sides are 4 and 7. The difference between 4 and 7 is 3, and the sum of 4 and 7 is 11, so the third side of the triangle must be greater than 3 and less than 11. This can be represented by the expression 3 < x < 11. Use these values to create a range for the possible perimeter of the triangle. If the third side of the triangle is 3, and the other two sides are 4 and 7, the perimeter is 3 + 4 + 7 = 14. If the third side of the triangle is 11, and the other two sides are 4 and 7, then the perimeter is 11 + 4 + 7 = 22. Because the third side of the triangle is greater than 3 and less than 11, the perimeter of the triangle must be greater than 14 and less than 22. This can be represented by the expression 14 < perimeter < 22. The only answer choices that fall in that range are (B), (C), and (D), which are the correct answers.
Remember the third side rule of triangles here, which is how to find possible lengths of the third side of a triangle when given the two other sides. The third side rule dictates that the length of the third side of a triangle must be greater than the difference, but less than the sum, of the length of the two known sides. In this particular problem, the two known sides are 4 and 7. The difference between 4 and 7 is 3, and the sum of 4 and 7 is 11, so the third side of the triangle must be greater than 3 and less than 11. This can be represented by the expression 3 < x < 11. Use these values to create a range for the possible perimeter of the triangle. If the third side of the triangle is 3, and the other two sides are 4 and 7, the perimeter is 3 + 4 + 7 = 14. If the third side of the triangle is 11, and the other two sides are 4 and 7, then the perimeter is 11 + 4 + 7 = 22. Because the third side of the triangle is greater than 3 and less than 11, the perimeter of the triangle must be greater than 14 and less than 22. This can be represented by the expression 14 < perimeter < 22. The only answer choices that fall in that range are (B), (C), and (D), which are the correct answers.
gmatclubot
Re: A triangle has sides 4, 7, and x. Which of the following could be the [#permalink]
03 Jun 2023, 04:00
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