ACT · Plane Geometry · Triangles and the Pythagorean theorem
Question act-q-00460
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The question
In a right triangle, the two legs have lengths 5 and 12. What is the length of the hypotenuse?
- 12
- 17
- 14
- 13
Show answer & worked solution
Answer: 13
Worked solution. By the Pythagorean theorem, hypotenuse = √(5² + 12²) = √(169) = 13. (You may also recognize this as a Pythagorean triple.)
Why each wrong choice is wrong. The trap distractor adds the legs instead of using the Pythagorean theorem. Off-by-one distractors catch arithmetic slips.
Test-day tactic. Memorize the common Pythagorean triples. When you see one, you save the time of squaring and square-rooting.
About this question type
Items test the Pythagorean theorem, the special right triangles, similarity, and the triangle inequality.
You will see a question shaped like this one on roughly every other official ACT form, typically at the back end of the section, where the score gradient is steepest. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.