Question

Suppose you have 3 pieces of string measuring 6 inches, 9 inches, and 12 inches. How many unique triangles can you form with these pieces of string?

A. 0
B. 1
C. 2
D. Infinitely many

Answer 1

Let
x=12 in------------- > the longest of the three sides
y=6 in
z= 9 in
if x< (y+z)----------- > one unique triangle can be made
if x> (y+z)----------- > no triangle can be made
This is a Triangle Inequality Theorem
therefore
x=12
(y+z)=15
12<15------------ >one unique triangle can be made

the answer is the option B. 1