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# If the lengths of two sides of a certain triangle are 5 and 10, what

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If the lengths of two sides of a certain triangle are 5 and 10, what [#permalink]
Never mind, got it!
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Re: If the lengths of two sides of a certain triangle are 5 and 10, what [#permalink]
Can I translate "5 < x < 15" to "x has to be bigger than the smallest side, and smaller than the sum of the other two sides"??

Does this make sense?

Thanks.
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Re: If the lengths of two sides of a certain triangle are 5 and 10, what [#permalink]
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ramonguib wrote:
Can I translate "5 < x < 15" to "x has to be bigger than the smallest side, and smaller than the sum of the other two sides"??

Does this make sense?

Thanks.

Hi,
X has to be larger than the positive difference between the two other sides and smaller than the sum of the two other two sides.
10-5
In general, x can be smaller than the smallest known side. Eg 10 and 9 allows x to be between 1 and 19.

Not sure if this was what you asked?

Posted from my mobile device
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Re: If the lengths of two sides of a certain triangle are 5 and 10, what [#permalink]
For the first statement how come the third side not be 10√3?

If the triangle has angles 30-60-90 a possible scenario is 1-√3-2 for its sides.
Which will make the triangle to have a perimeter of : 5+10+10√3 = 5(1+2+√3)=5*(3+√3) which IS a multiple of 5.
Why am I wrong here?
Does the perimeter HAVE TO be an integer in order to be a multiple of 5?
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Re: If the lengths of two sides of a certain triangle are 5 and 10, what [#permalink]
arven wrote:
For the first statement how come the third side not be 10√3?

If the triangle has angles 30-60-90 a possible scenario is 1-√3-2 for its sides.
Which will make the triangle to have a perimeter of : 5+10+10√3 = 5(1+2+√3)=5*(3+√3) which IS a multiple of 5.
Why am I wrong here?
Does the perimeter HAVE TO be an integer in order to be a multiple of 5?

On the GMAT, 'multiple of x' refers only to integer multiples. So, 15 is a multiple of 5 (since it's 3*5) but 6 isn't a multiple of 5, even though 6 = 1.2*5.
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Re: If the lengths of two sides of a certain triangle are 5 and 10, what [#permalink]
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The key to solving this problem is the property of triangles: Given any two sides, the third side of the triangle is greater than the difference and lesser than the sum of the two given sides.
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Re: If the lengths of two sides of a certain triangle are 5 and 10, what [#permalink]
)Property of a triangle: The sum of any two sides of a triangle is always greater than the third side of the triangle.
So, the third side of triangle could take any value from 6 to 14(both inclusive).
Statement 1: This is only possible if the third side is also a multiple of 5 because the sum of other two sides is 15 i.e. a multiple of 5.
So, the only possible value for third side is 10. Hence, Sufficient.
Statement 2: Isosceles triangle has two equal sides.
Other 2 sides are 10 and 5. Third side can’t be 5 because then the sum of two sides (5 + 5) = 10(third side).
So, the only possible value of third side is 10. Hence, Sufficient.
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Re: If the lengths of two sides of a certain triangle are 5 and 10, what [#permalink]
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Bunuel please tag this as a GMATPrep question, thank you!
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Re: If the lengths of two sides of a certain triangle are 5 and 10, what [#permalink]
nhatanh811 wrote:
Bunuel please tag this as a GMATPrep question, thank you!

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Re: If the lengths of two sides of a certain triangle are 5 and 10, what [#permalink]
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Re: If the lengths of two sides of a certain triangle are 5 and 10, what [#permalink]
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