The converse of the Pythagorean theorem says that if the side lengths of a triangle satisfy the equation a² + b² = c², then the triangle is a right triangle. Which triangle is a right triangle?
15, 8, 17
15, 16, 17
15, 8, 9
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The converse of the Pythagorean theorem says that if the side lengths of a triangle satisfy the equation a² + b² = c², then the triangle is a right triangle. Which triangle is a right triangle?
15, 8, 17
15, 16, 17
15, 8, 9
To determine which triangle is a right triangle, we can use the converse of the Pythagorean theorem: If a² + b² = c², then the triangle is a right triangle, where c is the longest side.
Let’s check each set of side lengths:
1. 15, 8, 17:
( 15² + 8² = 225 + 64 = 289 )
( 17² = 289 )
Since ( 15² + 8² = 17² ), this is a right triangle.
2. 15, 16, 17:
( 15² + 16² = 225 + 256 = 481 )
( 17² = 289 )
Since ( 15² + 16² neq 17² ), this is not a right triangle.
3. 15, 8, 9:
( 15² + 8² = 225 + 64 = 289 )
( 9² = 81 )
Since ( 15² + 8² neq 9² ), this is not a right triangle.
Conclusion: The triangle with sides 15, 8, and 17 is a right triangle.