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The lengths of two sides of isosceles triangle XYZ are 8 and 18.

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GreenlightTestPrep
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The lengths of two sides of isosceles triangle XYZ are 8 and 18. [#permalink] New post   Updated on: 14 Feb 2021, 09:38
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The lengths of two sides of isosceles triangle XYZ are 8 and 18.


Quantity A
Quantity B
The perimeter of triangle XYZ
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.
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A

Originally posted by GreenlightTestPrep on 14 Feb 2021, 07:04.
Last edited by Carcass on 14 Feb 2021, 09:38, edited 1 time in total.
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Re: The lengths of two sides of isosceles triangle XYZ are 8 and 18. [#permalink] New post   14 Feb 2021, 09:11
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GreenlightTestPrep wrote:
The lengths of two sides of isosceles triangle XYZ are 8 and 18.


Quantity A
Quantity B
The perimeter of triangle XYZ
36


Any side in a triangle must be less than the sum of other 2 sides and at the same time must be greater than the positive difference between them.

Let the third side be \(x\)

So, \(18 - 8 < x < 18 + 8\)

\(10 < x < 26\)

Adding 18 and 8 in the inequality:

\(18 + 8 + 10 < 18 + 8 + x < 18 + 8 + 26\)

\(36 < Perimeter < 52\)

Clearly, Col. A > Col. B

Hence, option A
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Re: The lengths of two sides of isosceles triangle XYZ are 8 and 18. [#permalink] New post   14 Feb 2021, 10:01
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According to the question's assumption, the triangle is an ISOSCELES, which means 2 sides of the triangle should be equal. We have given 8 and 18, So the third side should be either 8 or 18. If two sides are 8, the perimeter of the triangle will be: 8 + 8 + 18 = 34 < 36. On the other hand, if two sides are 18, the perimeter of the triangle will be: 18 + 18 + 8 = 44 > 36. Hence, the answer is D.
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The lengths of two sides of isosceles triangle XYZ are 8 and 18. [#permalink] New post   14 Feb 2021, 11:59
GreenlightTestPrep wrote:
The lengths of two sides of isosceles triangle XYZ are 8 and 18.


Quantity A
Quantity B
The perimeter of triangle XYZ
36



Key property : If two sides of a triangle have lengths A and B, then . . .
the DIFFERENCE between A and B < length of third side < the SUM of A and B

Since an isosceles triangle has two the sides of equal length, there are two possible cases to consider:
case i: The three sides have lengths 8, 18 and 18
case ii: The three sides have lengths 8, 8 and 18

Important: case ii breaks the above property.
If we let the side with length 18 be the third side, we get: 8 - 8 < 18 < 8 + 8
Simplify to get: 0 < 18 < 16, which is not true.
So, case ii is impossible

Case i meets the above property, so the sides must have lengths 8, 18 and 18, which means the perimeter = 8 + 18 + 18 = 44

Answer: A
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Re: The lengths of two sides of isosceles triangle XYZ are 8 and 18. [#permalink] New post   14 Feb 2021, 12:54
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Re: The lengths of two sides of isosceles triangle XYZ are 8 and 18. [#permalink] New post   15 Feb 2021, 05:35
Mishra04 wrote:
D

The correct answer is A. See the explanations above.
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Re: The lengths of two sides of isosceles triangle XYZ are 8 and 18. [#permalink] New post   02 Jun 2021, 22:51
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We need to be very careful. In every Question, Test maker try to fool test taker. Here is the same case. Most of test taker in rush forget to check whether their is possibility of having third side 8 or not, eventually, tend to make mistake. Likewise, in another scenario, they started to stating QUESTION like figure are not drawn to scale just to make us tempting :lol
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Re: The lengths of two sides of isosceles triangle XYZ are 8 and 18. [#permalink] New post   20 Jan 2025, 10:20
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The lengths of two sides of isosceles triangle XYZ are 8 and 18. [#permalink]
20 Jan 2025, 10:20
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