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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Given four rods of length 1 meter, 3 meters, 5 meters, and 7
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03 Jan 2019, 10:29
03 Jan 2019, 10:29
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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters, how many different triangles can be made using one rod for each side?
A. 6
B. 4
C. 3
D. 2
E. 1
A. 6
B. 4
C. 3
D. 2
E. 1
Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7
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03 Jan 2019, 11:39
03 Jan 2019, 11:39
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ANS=E
this question can best be solved using the triangle strategy that states that: given 2 sides of a triangle, the 3rd side will be greater than the difference of the 2 known sides but less than their sum. To begin solving this question, take the two extreme values provided in the question, 1 and 7. With them, find the range for the 3rd side.
For 1 and 7,
7-1 < 3rd side < 7+1
6 < 3rd side < 8
Since neither 3 nor 5 fall in this range, the rod combinations of 1-5-7 and 1-3-7 cannot form a triangle. Definitely, 1 cannot be a side of the triangle.
Now try 3 and 7
7-3 < 3rd side < 7+3
4 < 3rd side < 10
Here, we observe that 5 falls within this range. Therefore the rod combination of 3-5-7 does indeed form a triangle. That counts as 1 triangle so far.
At this point you can infer and notice that when you try sides 5 and 7, you will obviously end up with a side being 3. However, let's just do it for the love of it.
Trying 5 and 7,
7-5 < 3rd side < 7+5
2 < 3rd side < 12
As we can see, 3 falls within this range. Note that the triangle formed is still the one with sides 3-5-7.
Therefore only 1 triangle can be formed from the given rods. Thus the answer is(E)
this question can best be solved using the triangle strategy that states that: given 2 sides of a triangle, the 3rd side will be greater than the difference of the 2 known sides but less than their sum. To begin solving this question, take the two extreme values provided in the question, 1 and 7. With them, find the range for the 3rd side.
For 1 and 7,
7-1 < 3rd side < 7+1
6 < 3rd side < 8
Since neither 3 nor 5 fall in this range, the rod combinations of 1-5-7 and 1-3-7 cannot form a triangle. Definitely, 1 cannot be a side of the triangle.
Now try 3 and 7
7-3 < 3rd side < 7+3
4 < 3rd side < 10
Here, we observe that 5 falls within this range. Therefore the rod combination of 3-5-7 does indeed form a triangle. That counts as 1 triangle so far.
At this point you can infer and notice that when you try sides 5 and 7, you will obviously end up with a side being 3. However, let's just do it for the love of it.
Trying 5 and 7,
7-5 < 3rd side < 7+5
2 < 3rd side < 12
As we can see, 3 falls within this range. Note that the triangle formed is still the one with sides 3-5-7.
Therefore only 1 triangle can be formed from the given rods. Thus the answer is(E)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7
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04 Jan 2019, 07:08
04 Jan 2019, 07:08
1
GreenlightTestPrep wrote:
Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters, how many different triangles can be made using one rod for each side?
A. 6
B. 4
C. 3
D. 2
E. 1
A. 6
B. 4
C. 3
D. 2
E. 1
IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and B
Let's focus on this part: length of third side < SUM of A and B
We can also say that the length of LONGEST side must be less than the SUM of the other two sides
Let's systematically go through all possible combinations of 3 sides
case a) the LONGEST side has a length of 7 meters
So, 7 must be less than the SUM of the other two sides
This means the remaining 2 sides must have lengths 3 and 5 meters
So, a triangle with lengths 3-5-7 is POSSIBLE
This is the ONLY possible configuration in which the LONGEST side has a length of 7 meters
case b) the LONGEST side has a length of 5 meters
So, 5 must be less than the SUM of the other two (shorter) sides
If 5 is the longest side, then the other 2 sides must have lengths of 1 and 3 meters
HOWEVER, this breaks our rule that says the length of LONGEST side must be less than the SUM of the other two sides
So, we CANNOT have a triangle in which the LONGEST side has a length of 5 meters
case c) the LONGEST side has a length of 3 meters
This cannot work, since there's only one rod that has a length that's less than 1
case d) the LONGEST side has a length of 1 meters
This cannot work
So, there's only 1 possible triangle that can be created.
Answer: E
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