Question

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.'

Answer 1

The perimeter is 7 dm

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<4 dm

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