The lengths of all sides of a triangle are integers when measured in decimeters. one of the sides has length of 1 dm and another of 3 dm. find the perimeter of the triangle.'

The perimeter is 7 dm

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let

c> the length of the third side

case a)

1+c>3

c>2 dm

case b)

1+3> c

4 > c

rewrite

c

The solution for c is the interval> (2,4)

therefore

the value of c must be equal to

c=3 dm (because is an integer)

The perimeter is equal to

P=1+3+3=7 dm

7 dm

Step-by-step explanation:

One side is 1 dm while the other is 3 dm, so first you should add 1 and 3 together, and you get 4. you know that the answer has to be an integer. if this is an isosceles triangle then the last side has to be either 1 or 3. the last step is to add all three sides together.

-Char-

You are not going to be able to find a numerical value of this triangle because you do not know the type of triangle or the other side length. You can represent the perimeter using algebra though.

To find the perimeter you add the lengths of all 3 sides.

To show this as an algebraic expression, you would put 1 dm + 3 dm + x.

This will simplify to x + 4 dm, where x is the length of the missing side (in decimeter).