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If 3 and 8 are the lengths of two sides of a triangular

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by Brent@GMATPrepNow » Sun Dec 01, 2019 6:10 am
BTGmoderatorLU wrote:Source: GMAT Paper Tests

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

The OA is A
IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
difference between sides A and B < third side < sum of sides A and B

So, for this question: 8 - 3 < third side < 8 + 3
Simplify: 5 < third side < 11

So, the third side must be LONGER than 5 and SHORTER than 11
Answer: A

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by Scott@TargetTestPrep » Mon Dec 09, 2019 5:36 pm
BTGmoderatorLU wrote:Source: GMAT Paper Tests

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

The OA is A
Since the sum of 2 of the sides of any triangle must be greater than the 3rd side, only 8 could be the length of the third side of the triangle.

Answer: A

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by [email protected] » Tue Dec 10, 2019 12:05 pm
Hi All,

We're told that 3 and 8 are the lengths of two sides of a triangular region. We're asked which of the following values (3, 8 and 11) could be the length of the third side. This question is based on the Triangle Inequality Theorem and requires just a little Arithmetic to solve.

To start, when you have two sides of a triangle, the SMALLEST the third side could be would be just a little bit MORE than the DIFFERENCE of the two sides you have. Here, that's 8 - 3 = 5. If the third side was EXACTLY 5, then you would NOT have a triangle - you'd have a line of 8 on top of another line of 8. By making that third side just a little bigger than 5, you would then have a triangle.

In that same way, the LARGEST the third side could be would be just a little bit LESS than the SUM of the two sides. Here, that's 3 + 8 = 11. If the third side was EXACTLY 11, then you would NOT have a triangle - you'd have a line of 11 on top of another line of 11. By making that third side just a little less than 11, you would then have a triangle.

Thus, that third side falls into the following range: 3 < third side < 11. Based on the three given options, only a side of 8 is possible.

Final Answer: A

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