ACT · Plane Geometry · Triangles and the Pythagorean theorem
Question act-q-00453
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The question
In a right triangle, the two legs have lengths 9 and 12. What is the length of the hypotenuse?
- 15
- 16
- 21
- 14
Show answer & worked solution
Answer: 15
Worked solution. By the Pythagorean theorem, hypotenuse = √(9² + 12²) = √(225) = 15. (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 a moderate position in the section — solidly within the range that separates a 600-band student from a 700-band student. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.