Classify the triangle based on the side lengths 4.2, 6.4 and 7.6.

1 Answer

  • The three sides are different from each other, so the triangle is scalene.

    To classify by angles, we must compare the square of the largest side with the sum of the squares of the other two. In a triangle with lenghts a, b and c (with c>a and c>b):
    If [tex]c^2<a^2+b^2[/tex], the triangle is acute.
    If [tex]c^2=a^2+b^2[/tex], the triangle is right.
    If [tex]c^2>a^2+b^2[/tex], the triangle is obtuse.

    In this problem:

    [tex]7.6^2=57.76~~\text{and}~~4.2^2+6.4^2=17.64+40.96=58.6\\\\ \text{So}~~7.6^2\ \textless \ 4.2^2+6.4^2\Longrightarrow \text{The triangle is \boxed{acute}.}[/tex]