Solution:
To figure out if a triangle with sides that measure 3 inches, 4 inches, and 5 inches, is a right triangle, we use the Pythagorean theorem.
According to the Pythagorean theorem, the square of the longest side of the triangle (hypotenuse) is equal to the sum of the squares of the other two sides (adjacent and opposite) of a right-triangle.
This implies that
[tex](hypotenuse)^2=(adjacent)^2+(opposite)^2[/tex]In this case, the longest side is 5 inches.
[tex]hypotenuse=5[/tex]Thus,
[tex]\begin{gathered} (hypotenuse)^2=3^2+4^2 \\ =9+16 \\ =25 \\ \end{gathered}[/tex]Since the sum of the squares of the two sides (adjacent and opposite) is exactly equal to the hypotenuse, we can conclude that the triangle is a right triangle.
