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Is the triangle shown here a right triangle?
publish date: 2025/10/28 06:47:28.801955 UTC
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Correct Answer
No
Explanation
We will substitute the side lengths, 6, 8, and 11, 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, 11, for \( c \), because it is the possible hypotenuse. The lengths of 6 and 8 may be substituted for either \( a \) or \( b \).
This is the Pythagorean equation.
\[ a^2 + b^2 = c^2 \]Substitute 6 for \( a \), 8 for \( b \), and 11 for \( c \)
\[ 6^2 + 8^2 \stackrel{?}{=} 11^2 \]Evaluate each exponential expression
\[ 36 + 64 \stackrel{?}{=} 121 \]This is a false statement
\[ 100 = 121 \]Since 100 ≠ 121, the right triangle is not a right triangle.
Reference
Mathematics for college students