Question: In triangle XYZ, if XY = 5 cm, YZ = 12 cm, and XZ = 13 cm, is triangle XYZ a right triangle?
Options:
Yes
No
Not enough information
Only if XY is the longest side
Correct Answer: Yes
Solution:
Triangle XYZ is a right triangle because 5² + 12² = 25 + 144 = 169 = 13².
In triangle XYZ, if XY = 5 cm, YZ = 12 cm, and XZ = 13 cm, is triangle XYZ a rig
Practice Questions
Q1
In triangle XYZ, if XY = 5 cm, YZ = 12 cm, and XZ = 13 cm, is triangle XYZ a right triangle?
Yes
No
Not enough information
Only if XY is the longest side
Questions & Step-by-Step Solutions
In triangle XYZ, if XY = 5 cm, YZ = 12 cm, and XZ = 13 cm, is triangle XYZ a right triangle?
Pythagorean Theorem – In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Triangle Inequality Theorem – The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
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