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length of the side of the triangle given the perimeter

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length of the side of the triangle given the perimeter

by gmattesttaker2 » Fri Feb 21, 2014 11:50 pm
Hello,

Can you please tell me how to solve this:

If the perimeter of a triangle is 18, then the length of one of the sides CANNOT be:

(A) l (B) 3 (C) 6 (D) 8 (E) 9

OA: E

Is this correct:

The length of any one side of the triangle cannot be greater than the length of the other 2 sides and cannot be less than the difference of the other 2 sides i.e. it has to be

a + b > c > a - b

where a, b and c are the 3 sides of the triangle.

But I was not sure how to apply this here.

Thanks for your help,
Sri
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by Uva@90 » Sat Feb 22, 2014 1:12 am
gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:

If the perimeter of a triangle is 18, then the length of one of the sides CANNOT be:

(A) l (B) 3 (C) 6 (D) 8 (E) 9

OA: E

Is this correct:

The length of any one side of the triangle cannot be greater than the length of the other 2 sides and cannot be less than the difference of the other 2 sides i.e. it has to be

a + b > c > a - b

where a, b and c are the 3 sides of the triangle.

But I was not sure how to apply this here.

Thanks for your help,
Sri
Sri,
What you did is correct,
a + b > c > a - b

If you stuck some where pick from answer and solve it.

for example take 6
if any one side is 6
then can a + b > c pass ? yes it is possible.

Let one side be 9 ,
then a + b > c rule fails,
Hence ans is E.

To the more, Each side of a triangle must be less than half the triangle's perimeter.

Regards,
Uva.
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by GMATGuruNY » Sat Feb 22, 2014 4:12 am
gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:

If the perimeter of a triangle is 18, then the length of one of the sides CANNOT be:

(A) l (B) 3 (C) 6 (D) 8 (E) 9

OA: E
THIRD-SIDE RULE:
The length of any side of a triangle must be LESS THAN THE SUM OF THE LENGTHS OF THE OTHER TWO SIDES.

Here, the perimeter = 18.
Test the greatest answer choice.
If one of the sides = 9, then the sum of the lengths of the other two sides = 9, violating the rule above.
Thus, a side of 9 is not possible.

The correct answer is E.
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by gmattesttaker2 » Sat Feb 22, 2014 9:53 am
Uva@90 wrote:
gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:

If the perimeter of a triangle is 18, then the length of one of the sides CANNOT be:

(A) l (B) 3 (C) 6 (D) 8 (E) 9

OA: E

Is this correct:

The length of any one side of the triangle cannot be greater than the length of the other 2 sides and cannot be less than the difference of the other 2 sides i.e. it has to be

a + b > c > a - b

where a, b and c are the 3 sides of the triangle.

But I was not sure how to apply this here.

Thanks for your help,
Sri
Sri,
What you did is correct,
a + b > c > a - b

If you stuck some where pick from answer and solve it.

for example take 6
if any one side is 6
then can a + b > c pass ? yes it is possible.

Let one side be 9 ,
then a + b > c rule fails,
Hence ans is E.

To the more, Each side of a triangle must be less than half the triangle's perimeter.

Regards,
Uva.

Hello Uva,

Thanks for the explanation.

If we take 1 as the length of a side then we get:

12 + 5 > 1 > 12 - 5

but this won't be valid. Hence, does this rule still apply here.

The same for 3

12 + 3 > 3 > 12 - 3

Thanks,
Sri
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by Uva@90 » Sat Feb 22, 2014 5:10 pm
Hello Uva,

Thanks for the explanation.

If we take 1 as the length of a side then we get:

12 + 5 > 1 > 12 - 5

but this won't be valid. Hence, does this rule still apply here.

The same for 3

12 + 3 > 3 > 12 - 3

Thanks,
Sri
Sri,

I admit that the Numbers you took, 1,5,12 fails for below condition.

a + b > c > a - b

But 1,8.5,8.5 passes the above rule. So any side of a triangle can be of side 1 when the perimeter is 18.

Choose the side of triangle in such a way that
Each side of a triangle must be less than half the triangle's perimeter.

Similarly for 12,3,3.

Regards,
Uva.[/quote]
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