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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
In triangle ABC, side AC has length 12, and side AB has length 5.
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24 Mar 2022, 05:34
24 Mar 2022, 05:34
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In triangle ABC, side AC has length 12, and side AB has length 5.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
length of side BC |
13 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In triangle ABC, side AC has length 12, and side AB has length 5.
[#permalink]
25 Mar 2022, 06:22
25 Mar 2022, 06:22
1
GreenlightTestPrep wrote:
In triangle ABC, side AC has length 12, and side AB has length 5.
Quantity A |
Quantity B |
length of side BC |
13 |
TIP: Some students will recognize that 5 and 12 are two measurements of the Pythagorean triple 5-12-13, BUT this doesn't necessarily mean that side BC has length 13.
If we only know the lengths of two sides of a triangle (without any additional information), then there are infinitely-many triangles that can be created using those two side lengths.
In the diagram below, the blue side has length 5, and the red side has length 12:
So, triangle ABC COULD have lengths 5, 12 and 13, in which case side BC has length 13.
However, side BC could also have lengths that are less than 13 and greater than 13.
Answer: D
Re: In triangle ABC, side AC has length 12, and side AB has length 5.
[#permalink]
27 Mar 2022, 18:48
27 Mar 2022, 18:48
From the law of triangle:
For a triangle ABC, IF we have the length for AC and AB, we can determine the length of BC, IF AC is > AB we have:-
\(AB - AC < BC < AC + AB\)
Hence \(12 - 5 < BC < 12 + 5\)
or, \(7 < BC < 17\)
Therefore, BC can be 13, more than 13 but less than 17 and less than 13 but more than 7.
Ans is D
For a triangle ABC, IF we have the length for AC and AB, we can determine the length of BC, IF AC is > AB we have:-
\(AB - AC < BC < AC + AB\)
Hence \(12 - 5 < BC < 12 + 5\)
or, \(7 < BC < 17\)
Therefore, BC can be 13, more than 13 but less than 17 and less than 13 but more than 7.
Ans is D
