If two sides of a triangle measure 12 and 7, which cannot be the perimeter of the triangle

A

if 12 is the longest and 7 is the shortest then that would mean the addition of another 7 would be 28, no matter the triangle it is impossible for the perimeter to equal 29

Hello Tovarmackenzie!

We can utilize the Triangle Inequality Theorem, Which states

A + B > C

A + C > B

B + C > A

With that said, we are going look for C.

We know that

12 + 7 > C

So

19 > C

OR

C < 19

So our 3rd leg has to be less than 19.

So if we make C = 18.999 and Sum up all the sides, 12 + 7 + 18.999 = 37.999

this means the max perimeter is 37.999 ... so we know D: 38 cannot be the perimeter.