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Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters
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Updated on: 30 Aug 2020, 04:42
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Bunuel 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
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.
Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters
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07 Feb 2019, 18:39
Expert Reply
Bunuel 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
Since the sum of 2 sides of a triangle must be greater than the 3rd, the only option for the three sides is {3, 5, 7}. We cannot use the rod of length 1 meter in forming any triangles; we can verify that in any choice of three sides including the rod of length 1, there are two sides where the sum of the lengths is less than the length of the third side.
Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters
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05 May 2019, 01:59
GMATPrepNow wrote:
Bunuel 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
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
Hi Brent,
Just a quick question . Is it sum of any two sides should be greater than third side. or is it the longest side only that needs to be considered? 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.
Re: Given four rods of length 1 meter, 3 meters, 5 meters, and 7 meters
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08 Dec 2020, 08:25
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