Question

Which of the following sets of numbers could be the lengths of the sides of a triangle?

A. 8 m, 8 m, 17 m
B. 8 m, 4 m, 2 m
C. 8 m, 16 m, 24 m
D. 8 m, 6 m, 4 m

Answer 1

In any triangle, the sum of two of the sides must always be greater than the 3rd side.
a) no good 8 + 8 is not greater than 17
b) no good 4 + 2 is not greater than 8
c) no good 8 + 16 is not greater than 24 (being equal is not enough)
d) good 8+6>4 , 8+4>6 and 6 + 4 >8

Only d) 8m, 6m 4m can be made into a triangle

Answer 2

The sum of the lengths of two shorter sides of a triangle must be greater than the length of the longest side.


`A. \\ 8+8\ \textgreater \ 17 \\ 16\ \textgreater \ 17 \\ false \\ \\ B. \\ 2+4\ \textgreater \ 8 \\ 6\ \textgreater \ 8 \\ false \\ \\ C. \\ 8+16\ \textgreater \ 24 \\ 24\ \textgreater \ 24 \\ false \\ \\ D. \\ 4+6\ \textgreater \ 8 \\ 10\ \textgreater \ 8 \\ true`

The answer is D.