Question 1205301
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<pre>

The necessary and sufficient condition for a triangle with side lengths "a", "b" and "c" to exist

is fulfillment of all three "triangle inequalities"

    a + b > c,
  
    a + c > b,

    b + c > a.


In your case, all three triangle inequalities are satisfied - hence, such triangle does exist.


It can be constructed using a compass and a straightedge (a standard procedure).
</pre>

Solved, with explanations.



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On triangle inequalities, &nbsp;see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Points-lines-and-rays/Points-and-Straight-Lines-basics.lesson>Points and Straight Lines basics</A> 

in this site, &nbsp;Theorem 2.


You will be surprised to learn that triangle inequalities are very first corollaries from the basic axioms of Geometry.



On basic procedures of constructing triangles using a compass and a straightedge see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Triangles/How-to-draw-a-congruent-triangle-using-a-compass-and-a-ruler.lesson>How to construct a triangle using a compass and a ruler</A> 

in this site.


Learn the subject from there.