Geometry and TrigonometryEasy–MediumPythagorean theorem: missing leg
Geometry and Trigonometry practice question
A right triangle has a hypotenuse of length 13 and one leg of length 5. What is the length of the other leg?
Answer: 12
The hypotenuse is the longest side, so the legs' squares add to its square: 5² + b² = 13², giving b² = 169 − 25 = 144 and b = 12.
Common wrong answers
- If you answered 8
- 8 is 13 − 5. The relationship is between squares, not the lengths themselves: √(169 − 25) = 12.
- If you answered 18
- 18 is 13 + 5. Side lengths don't add; squares do — and for a missing LEG, subtract: 13² − 5² = 144.
- If you answered 13.9
- That comes from adding 13² + 5² = 194 and taking the root. The 13 is the hypotenuse, so its square is the total; subtract 5² from it instead of adding.
More Geometry and Trigonometry questions
- Easy–Medium
A circle has a radius of 6. What is its area? (Use A = πr².) - Easy–Medium
A right triangle has legs of length 6 and 8. What is the length of the hypotenuse? - Easy–Medium
A circle has a radius of 5. What is its circumference? (Use C = 2πr.) - Easy–Medium
What is the midpoint of the segment joining the points (2, 3) and (8, 11)? - Easy–Medium
What is the measure, in degrees, of angle B? - Easy–Medium
What is the area, in square centimeters, of the trapezoid?
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