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The sum of the lengths of two sides of isosceles triangle K

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The sum of the lengths of two sides of isosceles triangle K [#permalink] New post 14 May 2018, 14:02
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The sum of the lengths of two sides of isosceles triangle K is 7. K has a side of length 4.

Quantity A
Quantity B
The perimeter of K
11


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.
[Reveal] Spoiler: OA

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Re: The sum of the lengths of two sides of isosceles triangle K [#permalink] New post 15 May 2018, 08:37
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It could be that the 3 sides are 4,4 and 3 or it could be that the three sides are 4,3,3
In the first case the perimeter would be 11 and in the second case the perimeter would be 10
option D
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Re: The sum of the lengths of two sides of isosceles triangle K [#permalink] New post 15 May 2018, 08:40
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Carcass wrote:
The sum of the lengths of two sides of isosceles triangle K is 7. K has a side of length 4.

Quantity A
Quantity B
The perimeter of K
11


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.


Given: The sum of the lengths of two sides of isosceles triangle K is 7. K has a side of length 4.
Here are 2 possible triangles that meet this condition:
Case a: The triangle has lengths 3, 3, and 4
Case b: The triangle has lengths 3.5, 3.5, and 4

Let's examine each case separately.

Case a: The triangle has lengths 3, 3, and 4
Here, the perimeter = 3 + 3 + 4 = 10
So, we get:
Quantity A: 10
Quantity B: 11
Quantity B is greater


Case b: The triangle has lengths 3.5, 3.5, and 4
Here, the perimeter = 3.5 + 3.5 + 4 = 11
So, we get:
Quantity A: 11
Quantity B: 11
The two quantities are equal

Answer: D

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Re: The sum of the lengths of two sides of isosceles triangle K [#permalink] New post 21 May 2018, 19:35
Is it also possible for this triangle to have lengths of 4, 4, 3?
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Re: The sum of the lengths of two sides of isosceles triangle K [#permalink] New post 22 May 2018, 00:13
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Please see the two explanations above. They are very clear.

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Re: The sum of the lengths of two sides of isosceles triangle K [#permalink] New post 22 May 2018, 05:05
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jen6 wrote:
Is it also possible for this triangle to have lengths of 4, 4, 3?


Yes, that's also possible.

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Brent
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Re: The sum of the lengths of two sides of isosceles triangle K   [#permalink] 22 May 2018, 05:05
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