Answer:
a) yes
b) no
c) no, please see my notes below.
d) no
Explanation:
The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
a) 3, 4, 5
Add up the two shortest sides:
3+4 = 7
7 > 5 (the longest side), so yes, this can be a triangle.
b) 5, 7, 12
Add up the shortest side:
5 + 7 = 12
12 is NOT greater than 12, so no, this can't be a triangle.
c) 3*4, 2, 5*8 (what is your teacher asking for?! Does s/he mean 3.4 or 3*4? That dot is in a very odd position.)
If s/he means 3*4 and 5*8, then the sides would be:
12, 2, 40
12+2 = 14
14 is NOT greater than 40, so it can't be a triangle.
If s/he means 3.4, 2, 5.8
3.4 + 2 = 5.4
5.4 is NOT greater than 5.8 so it can't be a triangle.
d) 6, 7, 14
6 +7 = 13
13 is NOT greater than 14, so no, this can't be a triangle.