Question

Find the range for the measurement of the third side of a triangle, x, given the measures of the two sides: 5m and 11m.
A. 6m < x < 16m
B. 5m < x < 11m
C. 6m < x < 16m
D. 7m < x < 17m

Answer 1

try using this triangle -> http://www.mathsisfun.com/geometry/triangles-interactive.html grab point C and make it 107 degrees, notice the legs AB and AC are about a ratio of 5 and 11 respectively

then move the point C to make the angle A bigger or smaller

Answer 2

so as angle A shrinks or expands..... how small do you think you can make the side BC?
how big do you think BC can get?

Answer 3

well... maybe 107 degrees may not suffice... anyhow the idea is to use C to make the legs AB and AC 5 and 11, so you can check

Answer 4

is it c?

Answer 5

hmm what makes you think is C?

Answer 6

see how far the angle can shrink? or expand? how big will the 3rd leg be when that happens? how small can it get? how big can it get?

Answer 7

3 and 16

Answer 8

im lost
lol

Answer 9

now if both lines touch each other, that is, we shrink the angle between them to 0, then you won't have a triangle, just 3 flat lines

so the 3rd leg will have to be \(\bf \ne 0;\ thus \ > 0\)

now if both lines expand fully and lay flat on their back, then you won't have a triangle either, just again, 3 flat lines

so the 3rd leg will have to be \(\bf \ne 16\ thus \ < 16\)

Answer 10

hmmm I mean.... \(\bf \ne 6; \ thus \ > 6\)

Answer 11

when the 2 lines have an angle of 0 between them, the 3rd leg will be the slack of 11-5, so 6