Problem Solving

if 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I) 5
II) 8
III) 11

A. II only
B. III only
C. I and II only
D. II and III only
E. I, II and III

Tx!

IMO E

stefsemaan wrote:if 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?

I) 5
II) 8
III) 11

A. II only
B. III only
C. I and II only
D. II and III only
E. I, II and III

Tx!

The rule of finding the potential third side of any triangle when given the other two lengths is: The third side must be smaller than the sum and greater than the difference.

So for this example,

8-3=5
8+3=11

Since the third side must be smaller than the sum, it has to be less than 11. So anything 11 and over can't be the answer. Knock off B D and E because those all contain III.

Since the third side must be greater than the difference, it has to be more than 5. So anything with 5 or less can't be the answer. Knock off C because it contains I.

The only answer choice left is II, and indeed 8 is between 6 and 10 (remember, greater than the difference but less than the sum).

Hope this helped!

The rule to be applied here is the sum of 2 sides of a triangle must be greater than the third side.
(A) 5: 3+5 = 8 = one side, violation of rule.
(B) 8: 8+8 = 16 > 3 and 3+8 = 11 > 8. No violation
(C) 11: 8+3 = 11 = third side, violation of rule.

Hence (B) is the answer.

(8 - 3) < length of third side < (8 + 3) so ans is A

Also for perimeter:

(8 + 3) < perimeter < (2 * (8 + 3))

Got really stranded/confused by the explanations?

Can any GMAT expert answer this with much more clarity?

One of the basic rules of a triangle:

Any side of a triangle is less than a sum of two other sides and more than their difference ( a < b + c, a > b - c; b < a + c, b > a - c; c < a + b, c > a - b ).

So like stated above the third sides we will call x. So it has to be greater than 8 - 3 = 5 and less than 8 + 3.

Therefore 5 < x < 11. The only choice that fits is 8 Therfore the answer is A

Hope that helps

This is a property of triangle, Kartik...

in a triangle the third side cannot be greater than or equal to the addition of the first two sides. in this case the 2 sides are 3 and 8.

So the third side cannot have a length of 11 or greater, otherwise Kartik a triangle will not be formed. (try this on a graph paper).

Also in a triangle the third side cannot be less than or equal to the subtraction of the first two sides.

In this case the third side cannot be equal to or less than 5.

Hence the answer can only be 8.

The guyzz above have made a mistake, in marking the option as well.

The original answer is A i.e the option saying II only...

I hope Kartik this helped you...

Amit thanks for the crystal clear explanation.

[email protected] wrote:This is a property of triangle, Kartik...

in a triangle the third side cannot be greater than or equal to the addition of the first two sides. in this case the 2 sides are 3 and 8.

So the third side cannot have a length of 11 or greater, otherwise Kartik a triangle will not be formed. (try this on a graph paper).

Also in a triangle the third side cannot be less than or equal to the subtraction of the first two sides.

In this case the third side cannot be equal to or less than 5.

Hence the answer can only be 8.

The guyzz above have made a mistake, in marking the option as well.

The original answer is A i.e the option saying II only...

I hope Kartik this helped you...

Thank you very much for your clarification

seal4913 wrote:One of the basic rules of a triangle:

Any side of a triangle is less than a sum of two other sides and more than their difference ( a < b + c, a > b - c; b < a + c, b > a - c; c < a + b, c > a - b ).

So like stated above the third sides we will call x. So it has to be greater than 8 - 3 = 5 and less than 8 + 3.

Therefore 5 < x < 11. The only choice that fits is 8 Therfore the answer is A

Hope that helps