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Is the triangle shown here a right triangle?
publish date: 2025/10/28 06:55:53.522072 UTC
volume_mute
Correct Answer
Yes
Explanation
We will substitute the side lengths, 48, 55, and 73, into the Pythagorean equation \( a^2 + b^2 = c^2 \). By the converse of the Pythagorean theorem, the triangle is a right triangle if a true statement results. The triangle is not a right triangle if a false statement results.
We must substitute the longest side length, 73, for \( c \), because it is the possible hypotenuse. The lengths of 48 and 55 may be substituted for either \( a \) or \( b \).
This is the Pythagorean equation.
\[ a^2 + b^2 = c^2 \]Substitute 48 for \( a \), 55 for \( b \), and 73 for \( c \)
\[ 48^2 + 55^2 \stackrel{?}{=} 73^2 \]Evaluate each exponential expression
\[ 2,304 + 3,025 \stackrel{?}{=} 5,329 \]This is a true statement
\[ 5,329 = 5,329 \]Since 100 = 121, the right triangle is a right triangle.
Reference
Mathematics for college students