SOLUTION: Karen says that there is only one triangle with sides of 3 inches, 4 inches and 5 inches. Mika says that there can be many different triangles with those measures. Who is corre

Algebra ->  Triangles -> SOLUTION: Karen says that there is only one triangle with sides of 3 inches, 4 inches and 5 inches. Mika says that there can be many different triangles with those measures. Who is corre      Log On


   

Question 1180981: Karen says that there is only one triangle with sides of 3
inches, 4 inches and 5 inches. Mika says that there can be many different
triangles with those measures. Who is correct? Explain your reasoning.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Any three side lengths either determine a single triangle, or they don't form a triangle at all.

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

With three given sides lengths, two opportunities are possible: 

    - either NO ONE TRIANGLE with the given side lengths does exist (if the triangle inequalities are violated)


    - OR infinitely many such triangles do exists, but they all are congruent.


With the given sides of 3, 4 and 5 inches, you have classic right-angled triangle.

There are infinitely many such triangles in a plane, and they all are congruent.