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 BLet's focus on this part:
length of third side < SUM of A and BWe can also say that
the length of LONGEST side must be less than the SUM of the other two sidesHi 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 sidesThis 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) sidesIf 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 sidesSo, 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
RELATED VIDEO FROM OUR COURSE