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The lengths of two sides of isosceles triangle XYZ are 8 and 18.
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Updated on: 14 Feb 2021, 09:38
Updated on: 14 Feb 2021, 09:38
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The lengths of two sides of isosceles triangle XYZ are 8 and 18.
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 |
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.
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.
Last edited by Carcass on 14 Feb 2021, 09:38, edited 1 time in total.
Updated
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Re: The lengths of two sides of isosceles triangle XYZ are 8 and 18.
[#permalink]
14 Feb 2021, 09:11
14 Feb 2021, 09:11
1
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
Re: The lengths of two sides of isosceles triangle XYZ are 8 and 18.
[#permalink]
14 Feb 2021, 10:01
14 Feb 2021, 10:01
3
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.
