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The perimeter of a triangle $A B C$ is 25 units. Which of the followin
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11 Aug 2025, 10:22
11 Aug 2025, 10:22
Expert Reply
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Question Stats:
20% (01:30) correct
80% (01:25) wrong based on 5 sessions
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The perimeter of a triangle $\(A B C\)$ is 25 units. Which of the following options cannot be the length of one of the sides in the triangle?
Indicate all that apply
\(\boxed{A}\) $\(A B=10\)$ units
\(\boxed{B}\) $\(A C=13\)$ units
\(\boxed{C}\) $\(B C=12\)$ units
\(\boxed{D}\) $\(A B=18\)$ units
Indicate all that apply
\(\boxed{A}\) $\(A B=10\)$ units
\(\boxed{B}\) $\(A C=13\)$ units
\(\boxed{C}\) $\(B C=12\)$ units
\(\boxed{D}\) $\(A B=18\)$ units
Re: The perimeter of a triangle $A B C$ is 25 units. Which of the followin
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30 Aug 2025, 08:06
30 Aug 2025, 08:06
Expert Reply
The perimeter of triangle $A B C$ is 25 units, so:
$$
\(A B+B C+C A=25\)
$$
The Triangle Inequality Theorem states that the length of any one side must be less than the sum of the other two sides.
Also, the length of any side must be less than half the perimeter:
$$
\(\text { Each side }<\frac{25}{2}=12.5\)
$$
Let's check each option:
- A: $A B=10$ units - This is less than 12.5, so possible.
- B : $A C=13$ units - This is greater than 12.5 , which violates the side length condition. Not possible.
- C : $B C=12$ units - This is less than 12.5, possible.
- D : $A B=18$ units - This is greater than 12.5 , which violates the side length condition. Not possible.
Thus, the side lengths that cannot be sides of the triangle are $A C=13$ units and $A B=$ 18 units.
The answers are B and D.
$$
\(A B+B C+C A=25\)
$$
The Triangle Inequality Theorem states that the length of any one side must be less than the sum of the other two sides.
Also, the length of any side must be less than half the perimeter:
$$
\(\text { Each side }<\frac{25}{2}=12.5\)
$$
Let's check each option:
- A: $A B=10$ units - This is less than 12.5, so possible.
- B : $A C=13$ units - This is greater than 12.5 , which violates the side length condition. Not possible.
- C : $B C=12$ units - This is less than 12.5, possible.
- D : $A B=18$ units - This is greater than 12.5 , which violates the side length condition. Not possible.
Thus, the side lengths that cannot be sides of the triangle are $A C=13$ units and $A B=$ 18 units.
The answers are B and D.
gmatclubot
Re: The perimeter of a triangle $A B C$ is 25 units. Which of the followin [#permalink]
30 Aug 2025, 08:06
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