A right triangle has hypotenuse 17 cm and one leg 8 cm. Find the other leg.
Incorrect answer: √353 cm
For a missing leg, subtract squares; do not add them. Taking 13 − 5 also fails because the theorem relates squared lengths, not lengths directly.
Adding squares when finding a missing leg
The hypotenuse is already the sum-of-squares side. Subtract the known leg’s square before taking a square root.
The correction
15 cm
17² − 8² = 289 − 64 = 225; √225 = 15.
- Confirm the triangle has a right angle and identify the hypotenuse.
- Write missing leg squared = hypotenuse squared − known leg squared.
- Take the positive square root and check that each leg is shorter than the hypotenuse.
Try the reasoning in another example
The hypotenuse is 10 m and one leg is 6 m. Find the other leg.
- b² = 100 − 36 = 64.
- Take the positive square root.
Answer: 8 m
Explain why each step preserves the quantity or relationship. If you can compute the answer but cannot explain the step, revisit the model before adding more questions.
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