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If the lengths of two sides of an isosceles triangle are 5 and 9, what

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If the lengths of two sides of an isosceles triangle are 5 and 9, what [#permalink]

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New post 01 Sep 2017, 06:44
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A
B
C
D
E

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  25% (medium)

Question Stats:

81% (00:28) correct 19% (00:33) wrong based on 35 sessions

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If the lengths of two sides of an isosceles triangle are 5 and 9, what is the length of the third side?

(A) 4
(B) 5
(C) 7
(D) 9
(E) cannot be determined
[Reveal] Spoiler: OA

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Re: If the lengths of two sides of an isosceles triangle are 5 and 9, what [#permalink]

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New post 01 Sep 2017, 07:04
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Bunuel wrote:
If the lengths of two sides of an isosceles triangle are 5 and 9, what is the length of the third side?

(A) 4
(B) 5
(C) 7
(D) 9
(E) cannot be determined


IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
|A-B| < third side < A+B

So, the third side of the triangle must satisfy this inequality.

Since we have an isosceles triangle, the third side must have length 5 or 9 AS LONG as it satisfies the inequality above

Can the third side have length 5?
Let's see...
|9 - 5| < 5 < 9 + 5
Simplify: 4 < 5 < 14
WORKS!

Can the third side have length 9?
Let's see...
|9 - 5| < 9 < 9 + 5
Simplify: 4 < 9 < 14
WORKS!

So, the third side can have length 5 OR 9

Answer:
[Reveal] Spoiler:
E


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Re: If the lengths of two sides of an isosceles triangle are 5 and 9, what [#permalink]

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New post 01 Sep 2017, 07:33
Bunuel wrote:
If the lengths of two sides of an isosceles triangle are 5 and 9, what is the length of the third side?

(A) 4
(B) 5
(C) 7
(D) 9
(E) cannot be determined


Isosceles triangle may have equal side as 5 or 9.
If equal sides are 5, the sides of triangle is 5, 5, 9
Lets check the validity of this triangle.
5+5>9
5+9>5
So this triangle is valid.

If equal sides are 9, the sides of triangle is 9, 9, 5
Lets check the validity of this triangle.
9+9>5
5+9>9
So this triangle is valid.

Both triangle is possible.

So, Answer E is correct
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Kudos [?]: 140 [0], given: 64

Re: If the lengths of two sides of an isosceles triangle are 5 and 9, what   [#permalink] 01 Sep 2017, 07:33
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