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

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Bunuel
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If the lengths of two sides of an isosceles triangle are 5 and 9, what [#permalink] New post  01 Sep 2017, 07:44
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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
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BrentGMATPrepNow
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If the lengths of two sides of an isosceles triangle are 5 and 9, what [#permalink] New post  Updated on: 26 May 2021, 05:55
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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: E

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Originally posted by BrentGMATPrepNow on 01 Sep 2017, 08:04.
Last edited by BrentGMATPrepNow on 26 May 2021, 05:55, edited 1 time in total.
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Re: If the lengths of two sides of an isosceles triangle are 5 and 9, what [#permalink] New post  01 Sep 2017, 08:33
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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ScottTargetTestPrep
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Re: If the lengths of two sides of an isosceles triangle are 5 and 9, what [#permalink] New post  27 May 2019, 18:59
Expert Reply
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



Since the triangle is isosceles, we see that the side lengths could be either 5-5-9 or 9-9-5.

Answer: E
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Re: If the lengths of two sides of an isosceles triangle are 5 and 9, what [#permalink] New post  27 May 2019, 19:06
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


Answer can be both 5 5 9 and 9 9 5 so CBD. E
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MathRevolution
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Re: If the lengths of two sides of an isosceles triangle are 5 and 9, what [#permalink] New post  20 Apr 2021, 00:20
Expert Reply
Rule 1: Isosceles triangle has two sides equal therefore the third side will be either 5 or 9 and also it must satisfy Rule 2 and Rule 3.

Rule 2: The sum of the two sides of the triangle is greater than the third side.

Rule 3: The difference between the two sides of the triangle is smaller than the third side.


Case I: The third side is 5-> Sides are 5,5,9 - Rule 1 Satisfied.

Rule 2: 9 + 5 > 5 - Satisifed

Rule 3: 9 - 5 < 5 - Satisifed


Case II: The third side is 5-> Sides are 5,9,9 - Rule 1 Satisfied.

Rule 2: 9 + 5 > 9 - Satisifed

Rule 3: 9 - 5 < 9 - Satisifed

So, the third side can be 5 or 9.

Answer E
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Re: If the lengths of two sides of an isosceles triangle are 5 and 9, what [#permalink]
20 Apr 2021, 00:20
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