BTGmoderatorDC 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
OA E
Source: Princeton Review
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
