Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryMedium
A carpenter needs to cut a piece of wood in the shape of a right-angled triangle. If one leg measures 6 inches and the hypotenuse measures 10 inches, what is the length of the other leg?
- A4 inches
- B8 inches
- C12 inches
- D7 inches
Show answer & explanationAnswer & explanation
Correct answer: B. 8 inches
For a right-angled triangle, the Pythagorean theorem states a² + b² = c², where a and b are the legs and c is the hypotenuse. Given a = 6 and c = 10, we have 6² + b² = 10², which simplifies to 36 + b² = 100. Subtracting 36 from both sides gives b² = 64, so b = √64 = 8 inches.
Why the other options are wrong
- A. Incorrect. This would be the difference (10-6), not the result of the Pythagorean theorem.
- C. Incorrect. This would be the hypotenuse if the legs were 6 and some other value, or if 10 was a leg and 6 was the other, which is not the case.
- D. Incorrect. This is not a Pythagorean triple result.
Pythagorean Theorem (finding a leg)
In a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (legs, a and b): a² + b² = c².
- Only applies to right-angled triangles.
- Used to find an unknown side length when two sides are known.
- Hypotenuse is always the longest side, opposite the right angle.
Memory trick: Hypotenuse is 'High', the legs 'Lie' on the ground.