If ABC is a isosceles triangle and if the sum of the lengths of its tw

Question

If ABC is a isosceles triangle and if the sum of the lengths of its two sides is 12 units, which of the following could be the length of the third side?

I. 1
II. 10
III. 11

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

M37-91

Bunuel · Accepted Answer

Official Solution:

If ABC is a isosceles triangle and if the sum of the lengths of its two sides is 12 units, which of the following could be the length of the third side?
 
I. 1 unit
 
II. 10 units
 
III. 11 units

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

To solve this question recall the following property:  the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides .
 
Notice that if the lengths of two equal sides are 6 and 6, then each option satisfies the above property: (1, 6, 6); (10, 6, 6); (11, 6, 6).
 
Thus, I, II, and III could be the length of the third side.

Answer: E

Mohammadmo · Answer

12=2X
X=6
6+6> 1& 10& 11
All of them could be another side of the triangle.
Option E

Posted from my mobile device

Archit3110 · Answer

use ∆ 3rd side rule sum of two sides>3 rd side 
all three options valid
IMO E

TestPrepUnlimited · Answer

By the triangle inequality, any side must be less than the sum of the other two sides, so the third side must be less than 12. We have found a upper bound for the third side and this does not eliminate any options.

Also by the triangle inequality, any side must be bigger than the difference of the other two sides. We only know two sides add up to 12, therefore we can find the lower bound of the third side by setting two sides as 6, which is gives us a lower bound of 0. 
 Finally, the third side must be between 0 and 12. All options are sufficient, we choose E.

Note the condition "isosceles triangle" cannot eliminate any options. We can have a 5, 7, 7 or 1, 11, 11 triangle for example and that does not limit any possibilities of the length of the third side.

ScottTargetTestPrep · Answer

Keep in mind that the sum of the lengths of two sides of a triangle must be greater than the length of the third side.

Since the sum of two sides is given to be 12, we see that 12 is greater than 1, 10, and 11. Thus, statements I, II, and III are all correct.

Answer: E

dcummins · Answer

I wasn't sure if the question was referring to the sum of the length of any two sides or the sum of the side of the equal angles. Can you make this a bit more clearer?

If ABC is a isosceles triangle and if the sum of the lengths of its tw

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If ABC is a isosceles triangle and if the sum of the lengths of its tw

Prep Toolkit

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