Question

Is it possible to draw a triangle with sides measuring 13, 21, and 39? Explain.

Answer 1

for a triangle to be possible it has to meet the following
\[a+b >c\]
\[a+c >b\]
\[b+c >a\]

Answer 2

13+21 bigger then 39? nope so, no triangle

Answer 3

The Side Inequality of triangle states "Sum of the lengths of any two sides of a triangle is more than the length of the third side".

So in such sums check if the sum of the two smaller sides is greater than the longest side or not ( sum of one of the smaller sides with the greatest side will obviously be greater than the third side).

Here the two smaller sides are 13 and 21, and their sum 34 < 39
so, no triangle is possible

Answer 4

yeah, consider your largest value to be a bar that you hold out in front of you; and you want the other parts attached to this, one at each end; i order to form a triangle; the length of the 2 shorter sides there add up to longer than the bar itself.

Answer 5

or, you are a distance from a friend/lover/bullfight/whatever; lets say that you are 39 miles apart and each start to walk towards each other

you walk a distance of 21 and the other walks a distance of 13

do you meet ?

Answer 6

No?

Answer 7

you are correct, but lets see why :)

39
-13
-----
26
-21
-----
5 ; you cant possibly meet since you are still 5 miles apart.

do you see how this relates to the triangle question?

Answer 8

add 5 and thats perfect estudier ;)