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If the lengths of two sides of an isosceles triangle are 5 and 9, what : Problem Solving (PS)
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# If the lengths of two sides of an isosceles triangle are 5 and 9, what

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

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