ACT · Plane Geometry · Triangles and the Pythagorean theorem
Question act-q-00457
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The question
In a right triangle, the two legs have lengths 3 and 4. What is the length of the hypotenuse?
- 6
- 5
- 7
- 4
Show answer & worked solution
Answer: 5
Worked solution. By the Pythagorean theorem, hypotenuse = √(3² + 4²) = √(25) = 5. (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.