Respuesta :

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.

38 cannot be the perimeter of the triangle.

What is Triangle Inequality Theorem?

The sum of any two sides of a triangle is greater than or equal to the third side.

Given:

Two sides are 12 and 7.

Using Triangle Inequality Theorem, we have

In ΔABC,

  • AB + BC > CA
  • AC + CB > BA
  • AB + CA > BC

So,

12 + 7 > C

19 > C

C < 19

So, the third side should be less than 19.

Let us take maximum possible values,

C  =18.999

Then, perimeter will be,

12 + 7 + 18.999 = 37.999

Hence, 38 cannot be the perimeter.

Learn more about Triangle Inequality Theorem here:

https://brainly.com/question/309896

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