ern5231 wrote:In a triangle, two sides are 5 and 10. What is the perimeter?
1) The perimeter is a multiple of 5
2) The triangle is isosceles

A value question . We need to find exact value of the perimeter.

1) The perimeter is a multiple of 5 .

We already know two sides are 5 and 10 . In order to form a triangle the third side should be greater than 5 (greater than positive difference between the two sides).

But that means 3rd side could be 10 , 15 , 20 ....

Accordingly perimeter will also change .

Insufficient .

2) The triangle is isosceles .

That means the 3rd side is equal to any of the two sides 5 or 10 . But the 3 rd side can not be 5 as sum of two sides has to be greater than the 3 rd side to form a triangle .

That means the 3rd side is 10 . Hence perimeter 25 .

[spoiler]Ans : B[/spoiler]

I dont agree with rocky in the first one
as the other side can not be 5 or 15 as

the sum of the two sides can not be smaller than the third one

if you put one side 5 the other 10 the other 15

the third side should be smaller than the sum of two and bigger than the substraction of the two sides this is a rule-sufficient

so it cant be 15 or 20

in the second choice it can be only 10 according to the first rule-sufficient

so IMO it is D

I dont agree with rocky in the first one
as the other side can not be 5 or 15 as

the sum of the two sides can not be smaller than the third one

if you put one side 5 the other 10 the other 15

the third side should be smaller than the sum of two and bigger than the substraction of the two sides this is a rule-sufficient

so it cant be 15 or 20

in the second choice it can be only 10 according to the first rule-sufficient

so IMO it is D

irmakyolcu wrote:I dont agree with rocky in the first one
as the other side can not be 5 or 15 as

the sum of the two sides can not be smaller than the third one

if you put one side 5 the other 10 the other 15

the third side should be smaller than the sum of two and bigger than the substraction of the two sides this is a rule-sufficient

so it cant be 15 or 20

in the second choice it can be only 10 according to the first rule-sufficient

so IMO it is D

Good catch!

Here's the rule:

for a triangle with sides a, b and c,

|b-c| < a < b + c
|a-c| < b < a + c
|a-b| < c < a + b

or, in English,

each side must be greater than the positive difference between the other two sides and less than the sum of the other two sides.

Applying the rule to the question above, we know that two sides are 5 and 10. If we call the 3rd side "x":

10 - 5 < x < 10 + 5
5 < x < 15

Since statement (1) tells us that x is a multiple of 5, we now know that x=10, so (1) is sufficient alone.

Similarly, looking at (2) we see that x = 5 or 10, but once we add in the above rule x must be 10, so (2) is also sufficient alone.